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物理代写|量子力学代写quantum mechanics代考|PHYSICS3544

Posted on 2023年3月29日2023年3月29日 by statistics-lab

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量子力学是物理学的一个基本理论，它在原子和亚原子粒子的尺度上对自然界的物理特性进行了描述。它是所有量子物理学的基础，包括量子化学、量子场论、量子技术和量子信息科学。

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Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

物理代写|量子力学代写quantum mechanics代考|PHYSICS3544

物理代写|量子力学代写quantum mechanics代考|Algebraic Lie Subalgebras of Special Phase Functions

We start by discussing distinguished Lie subalgebras of the Lie algebra of special phase functions, which are defined by means of algebraic conditions (see, also, $[227])$.

Proposition 12.6.1 The subsheaves of spacetime functions and of the projectable, time preserving and affine special phase functions (see Definition 12.1.3)
$\operatorname{map}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{aff} \operatorname{spe}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{tim} \operatorname{spe}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{prospe}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$
turn out to be closed with respect to the special phase Lie bracket.
Indeed, the following Lie subalgebra of special phase functions will play a role in the classification of infinitesimal symmetries of classical dynamics and in the discussion of classical currents (see Theorem 13.2.6 and Definition 13.3.1)

Now, let us choose a gauge $b$.
Definition 12.6.2 With reference to the gauge $b$, we define:

a short special phase functions to be a special phase functions $f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ such that $\hat{f}[b]=0$,
a quasi-short special phase function to be a special phase function $f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ such that $\hat{f}[b] \in \mathbb{R}$.

The subsheaves of short and quasi-short special phase functions are denoted by
$$
\operatorname{srt}{\mathrm{b}} \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) \subset \operatorname{srt}{\mathrm{b}}^{\prime} \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) \subset \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) . \quad \square
$$
Proposition 12.6.3 With reference to the gauge $b$, the short special phase functions $f \in \operatorname{srt}{\mathrm{b}} \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ are characterised by their tangent lift through the equality $$ f=-i{X[f]} A^{\uparrow}[\mathrm{b}]
$$
Accordingly, the sheaf of short special phase functions is constituted by the special phase functions of the the following type, with reference to any observer $o$,
$$
f=f^0 \mathcal{H}_0[\mathrm{~b}, o]+f^i \mathcal{P}_i[\mathrm{~b}, o], \quad \text { with } f^\lambda \in \operatorname{map}(\boldsymbol{E}, \mathbb{R}) \text {. }
$$

物理代写|量子力学代写quantum mechanics代考|Differential Lie Subalgebras of Special Phase

Next, we discuss distinguished Lie subalgebras of the Lie algebra of special phase functions, which are defined by means of differential conditions (see, also, [227]).
Preliminarily, we show that

the holonomic lift of special phase functions is a surjective Lie algebra morphism,
the hamiltonian lift of projectable special phase functions is a surjective Lie algebra morphism.
Then, we define and characterise the
quasi unitary Lie subalgebra of s.p.f. $f$, such that $d \operatorname{div}_\eta f=0$,
unitary Lie subalgebra of s.p.f. $f$, such that $\operatorname{div}_\eta f=0$,
holonomic Lie subalgebra of s.p.f. $f$, such that $X^{\uparrow}$ ham $[f]=X^{\uparrow}$ hol $[f]$,
conserved Lie subalgebra of s.p.f. $f$, such that $\gamma \cdot f=0$.
Proposition 12.6.5 For each $f, f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$, we have
$$
\left.\left[X^{\uparrow}{ }{\mathrm{hol}}[f], X{\mathrm{hol}}^{\uparrow}[f]\right]=X_{\mathrm{hol}}[\mathbb{I} f, f]\right]
$$
Hence, the holonomic lift of special phase functions (see Definition 12.3.2)
$$
X_{\text {hol }}^{\uparrow}: \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) \rightarrow \operatorname{hol} \sec \left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right): f \mapsto X^{\uparrow}{ }{\mathrm{hol}}[f] $$ turns out to be a surjective Lie algebra sheaf morphism, whose kernel is the subsheaf (see Proposition 12.3.3) $$ \operatorname{map}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) $$ Hence, the map $X^{\uparrow}$ hol passes to the quotient and we obtain a Lie algebra isomorphism $$ X{\text {hol }}^{\uparrow}: \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) / \operatorname{map}(\boldsymbol{E}, \mathbb{R}) \rightarrow \operatorname{hol} \sec (\boldsymbol{E}, T \boldsymbol{E})
$$

量子力学代考

物理代写|量子力学代写quantum mechanics代考|Algebraic Lie Subalgebras of Special Phase Functions

我们首先讨论特殊相函数李代数的不同李子代数，这些李子代数是通过代数条件定义的 (另见，[227]).
命题 12.6.1 时空函数的子层以及可投影、保时和仿射特殊相函数的子层 (见定义 12.1.3) $\operatorname{map}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{aff} \operatorname{spe}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{tim} \operatorname{spe}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{prospe}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ 结果对于特殊相位李括号是封闭的。
实际上，以下特殊相函数的李子代数将在经典动力学的无穷小对称性分类和经典电流的讨论中发挥作用 (参见定理 13.2.6 和定义 13.3.1)
现在，让我们选择一个仪表 $b$.
定义 12.6.2 参照量规 $b$ ，我们定义:

一个短的特殊相函数是一个特殊的相函数 $f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ 这样 $\hat{f}[b]=0$ ，
一个拟短的特殊相位函数是一个特殊相位函数 $f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ 这样 $\hat{f}[b] \in \mathbb{R}$.
短和准短特殊相函数的子层表示为
$$
\operatorname{srt} b \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) \subset \operatorname{srtb}^{\prime} \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) \subset \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)
$$
命题 12.6.3 关于量规 $b$, 短特殊相函数 $f \in \operatorname{srtb} \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ 的特点是通过平等他们的切线提升
$$
f=-i X[f] A^{\uparrow}[\mathrm{b}]
$$
因此，短特殊相函数的层由以下类型的特殊相函数构成，参考任何观察者 $O$ ，
$$
f=f^0 \mathcal{H}_0[\mathrm{~b}, o]+f^i \mathcal{P}_i[\mathrm{~b}, o], \quad \text { with } f^\lambda \in \operatorname{map}(\boldsymbol{E}, \mathbb{R})
$$

物理代写|量子力学代写quantum mechanics代考|Differential Lie Subalgebras of Special Phase

接下来，我们讨论特殊相函数李代数的不同李子代数，它们是通过微分条件定义的（另见 [227]）。初步地，我们表明

特殊相函数的完整提升是满射李代数态射，
可投影特殊相函数的哈密顿提升是满射李代数态射。
然后，我们定义和表征
$s p f$ 的拟酉李子代数 $f$, 这样 $d \operatorname{div}_\eta f=0$,
$\operatorname{spf}$ 的酉李子代数 $f$, 这样 $\operatorname{div}_\eta f=0$,
spf的完整李子代数 $f$, 这样 $X^{\uparrow}$ 也 $[f]=X^{\uparrow}$ 在哪里 $[f]$,
spf 的守恒李子代数 $f$, 这样 $\gamma \cdot f=0$.
命题 12.6.5 对于每个 $f, f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ ，我们有
$$
\left.\left[X^{\uparrow} \operatorname{hol}[f], X \operatorname{hol}^{\uparrow}[f]\right]=X_{\mathrm{hol}}[\mathbb{I} f, f]\right]
$$
因此，特殊相函数的完整提升（见定义 12.3.2）
$$
X_{\text {hol }}^{\uparrow}: \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) \rightarrow \operatorname{hol} \sec \left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right): f \mapsto X^{\uparrow} \operatorname{hol}[f]
$$
结果是满射李代数层态射，其内核是子层（见命题 12.3.3)
$$
\operatorname{map}(\boldsymbol{E}, \mathbb{R}) \subset \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)
$$
因此，地图 $X^{\uparrow} \mathrm{hol}$ 传递给商，我们得到一个李代数同构
$$
X \operatorname{hol}^{\uparrow}: \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) / \operatorname{map}(\boldsymbol{E}, \mathbb{R}) \rightarrow \operatorname{hol} \sec (\boldsymbol{E}, T \boldsymbol{E})
$$

物理代写|量子力学代写quantum mechanics代考请认准statistics-lab™

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R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
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物理代写|量子力学代写quantum mechanics代考|PHYS3040

Posted on 2023年3月29日2023年3月29日 by statistics-lab

如果你也在怎样代写量子力学quantum mechanics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的量子力学quantum mechanics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

物理代写|量子力学代写quantum mechanics代考|Hamiltonian Phase Lift of s.p.f.

Let us recall the hamiltonian phase lift $X^{\uparrow}$ ham $[f]:=\gamma\left(f^{\prime \prime}\right)+\Lambda^{\ddagger}(d f)$ of a generic phase function $f \in \operatorname{map}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ (see Definition 11.3.6).

Indeed, we can specialise the above hamiltonian lift of generic phase functions to special phase functions. We notice that, in the particular case of special phase functions, the above time scale $f^{\prime \prime}$ (see Lemma 11.3.5), coincides with the time component defined in Definition 12.1.1.

We stress that this phase lift resembles the standard hamiltonian lift in symplectic structures, but involves an additional unusual “horizontal” term which is related to the odd dimension of phase space. Moreover, we emphasise that the hamiltonian phase lift of special phase functions involves essentially the coPoisson structure $(\gamma, \Lambda)$ (or, equivalently, the cosymplectic structure $(d t, \Omega)$ ) of phase space.

Definition 12.4.1 For each $f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$, we define the hamiltonian phase lift to be the phase vector field
$$
X^{\uparrow}{ }{\operatorname{ham}}[f]:=\gamma\left(f^{\prime \prime}\right)+\Lambda^{ \pm}(d f) \in \operatorname{prosec}\left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right) \subset \sec \left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right) $$ which is projectable on the tangent lift $X[f] \in \sec (\boldsymbol{E}, T \boldsymbol{E})$. We denote the hamiltonian phase lift sheaf morphism and the subsheaf of hamiltonian phase lifts of all special phase functions, respectively, by $$ \begin{aligned} & X^{\uparrow}{ }{\text {ham }}: \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) \rightarrow \text { ham sec }\left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right): f \mapsto X^{\uparrow}{ }{\text {ham }}[f], \ & \text { ham } \sec \left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right) \subset \sec \left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right) \text {. } \ & \end{aligned} $$ Proposition 12.4.2 For each $f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$, we have the coordinate expression (see Corollary 11.3.7, Definition 3.2.9 and Theorem 10.1.8) $$ \begin{aligned} X^{\uparrow}{ }{\text {ham }}[f]=f^0 & \partial_0-f^i \partial_i+G_0^{i j}\left(-f^0\left(\partial_0 \mathcal{P}_j-\partial_j A_0\right)+f^h\left(\partial_h \mathcal{P}_j-\partial_j A_h\right)\right. \
& \left.+\partial_j f^0 \mathcal{K}_0+\partial_j f^h \mathcal{Q}_h+\partial_j \tilde{f}\right) \partial_i^0
\end{aligned}
$$

物理代写|量子力学代写quantum mechanics代考|Special Phase Lie Bracket

Several results of our approach suggest a special Lie bracket of special phase functions
$$
\mathbb{f}, f, f \mathbb{|} \mathbb{=}{f, f}+\gamma\left(f^{\prime \prime}\right) \cdot \dot{f}-\gamma\left(f^{\prime \prime}\right) \cdot f,
$$
which is given by the Poisson bracket plus an additional “horizontal” term (see Definition 11.4.1).

We stress that, in the particular case of affine special phase functions, the special Lie bracket reduces to the Poisson Lie bracket.

Here, we provide a direct definition of the special phase Lie bracket. But it is striking that, later, we might recover it by an independent procedure in a different quantum context, via the classification of $\eta$-hermitian quantum vector fields (see Theorem 19.1.7).

We observe that the Poisson Lie bracket of all phase functions does not carry full information of the geometric structure of the phase space, because it is achieved via the vertical phase 2-vector $\Lambda$ (see Corollary 9.2.4 and Remark 10.2.3).

The special Lie bracket is obtained via the pair $(\gamma, \Lambda)$, or, equivalently, via the pair $(d t, \Omega)$, which carry full information on the geometric structure of phase space (see Theorems 10.1.1 and 10.2.1 and, Appendix: Theorem I.1.11). Clearly, the special Lie bracket $\llbracket f, f \rrbracket$ carries also full information on gravitational and electromagnetic fields postulated in our theory.

Indeed, the special phase Lie bracket plays a fundamental role in our approach. We notice that an analogous special phase Lie bracket can be achieved in the einsteinian framework (see [220]).

Definition 12.5.1 For each $f, f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$, we define their special phase bracket to be the special phase function (see Theorems 9.2.6 and 9.2.11, Definition 12.1.1 and Lemma 11.3.5)
$$
\llbracket f, f \mathbb{f} \rrbracket:=\Lambda(d f, d f)+\gamma\left(f^{\prime \prime}\right) \cdot f-\gamma\left(f^{\prime \prime}\right) \cdot f
$$

量子力学代考

物理代写|量子力学代写quantum mechanics代考|Hamiltonian Phase Lift of s.p.f.

让我们回忆一下哈密顿相位提升 $X^{\uparrow}$ 也 $[f]:=\gamma\left(f^{\prime \prime}\right)+\Lambda^{\ddagger}(d f)$ 通用相函数 $f \in \operatorname{map}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ (见定义 11.3.6)。
实际上，我们可以将上述通用相函数的哈密顿提升专门化为特殊相函数。我们注意到，在特殊相函数的特殊情况下，上述时间尺度 $f^{\prime \prime}$ (见引理 11.3.5) ，与定义 12.1.1 中定义的时间分量一致。
我们强调，这个相位提升类似于辛结构中的标准哈密顿提升，但涉及一个额外的不寻常的”水平”项，它与相空间的奇数维有关。此外，我们强调特殊相位函数的哈密顿相位提升本质上涉及余泊松结构 $(\gamma, \Lambda)$ (或者，等效地，余辛结构 $(d t, \Omega))$ 的相空间。
定义 12.4.1 对于每个 $f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ ，我们将哈密尔顿相位提升定义为相位矢量场
$$
X^{\uparrow} \operatorname{ham}[f]:=\gamma\left(f^{\prime \prime}\right)+\Lambda^{ \pm}(d f) \in \operatorname{prosec}\left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right) \subset \sec \left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right)
$$
可投影在切线升力上 $X[f] \in \sec (\boldsymbol{E}, T \boldsymbol{E})$. 我们分别表示所有特殊相函数的哈密顿相位提升层态射和哈密顿相位提升的子层
$X^{\uparrow}$ ham $: \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right) \rightarrow$ ham sec $\left(J_1 \boldsymbol{E}, T J_1 \boldsymbol{E}\right): f \mapsto X^{\uparrow}$ ham $[f], \quad$ ham $\sec \left(J_1 \boldsymbol{E}, T J_1\right.$
命题 12.4.2 对于每个 $f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right.$ ，我们有坐标表达式（见推论 11.3.7，定义 3.2.9 和定理 $10.1 .8)$
$X^{\uparrow} \operatorname{ham}[f]=f^0 \partial_0-f^i \partial_i+G_0^{i j}\left(-f^0\left(\partial_0 \mathcal{P}_j-\partial_j A_0\right)+f^h\left(\partial_h \mathcal{P}_j-\partial_j A_h\right) \quad+\partial_j f^0 \mathcal{K}_0+\dot{c}\right.$

物理代写|量子力学代写quantum mechanics代考|Special Phase Lie Bracket

我们方法的几个结果表明特殊相函数的特殊李括号
$$
\mathrm{f}, f, f \mid=f, f+\gamma\left(f^{\prime \prime}\right) \cdot \dot{f}-\gamma\left(f^{\prime \prime}\right) \cdot f
$$
它由泊松括号加上附加的“水平”项给出（见定义 11.4.1）。
我们强调，在仿射特殊相函数的特殊情况下，特殊李括号简化为泊松李括号。
在伩里，我们提供了特殊相李括号的直接定义。但令人惊讶的是，后来，我们可能会在不同的量子环境中通过一个独立的程序恢复它，通过对 $\eta$-hermitian 量子矢量场（见定理 19.1.7）。
我们观察到所有相函数的泊松李括号不携带相空间几何结构的完整信息，因为它是通过垂直相 2-向量实现的 $\Lambda$ (参见推论 9.2.4 和备注 10.2.3)。
特殊的李括号是通过对获得的 $(\gamma, \Lambda)$ ，或者，等价地，通过对 $(d t, \Omega)$ ，其中包含有关相空间几何结构的完整信息 (参见定理 10.1.1 和 10.2.1 以及附录：定理 I.1.11）。显然，特殊的李括号 $\backslash$ llbracket $f, f \backslash$ rrbracket还包含我们理论中假设的引力场和电磁场的完整信息。
事实上，特殊相李括号在我们的方法中起着基础性的作用。我们注意到，在爱因斯坦框架中可以实现类似的特殊相位李括号（参见 [220]）。
定义 12.5.1 对于每个 $f, f \in \operatorname{spe}\left(J_1 \boldsymbol{E}, \mathbb{R}\right)$ ，我们将它们的特殊相位括号定义为特殊相位函数（参见定理 9.2.6 和 9.2.11，定义 12.1.1 和引理 11.3.5)
$\backslash$ llbracket $f, f \mathrm{f} \backslash$ rrbracket $:=\Lambda(d f, d f)+\gamma\left(f^{\prime \prime}\right) \cdot f-\gamma\left(f^{\prime \prime}\right) \cdot f$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

物理代写|电动力学代写electromagnetism代考|ELEC3104

Posted on 2023年3月29日2023年3月29日 by statistics-lab

如果你也在怎样代写电动力学electrodynamics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

电动力学是物理学的一个分支，处理快速变化的电场和磁场。

statistics-lab™ 为您的留学生涯保驾护航在代写电动力学electrodynamics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写电动力学electrodynamics代写方面经验极为丰富，各种代写电动力学electrodynamics相关的作业也就用不着说。

我们提供的电动力学electrodynamics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

物理代写|电动力学代写electromagnetism代考|Wave Mechanics and Electromagnetism

By way of introduction we consider the case of a particle in an external classical electromagnetic field according to wave mechanics. The wave function for a particle in a coordinate representation $\psi(x)$ is a complex-valued function of the space-time coordinates, $x=(\mathbf{r}, t)$. The phase of the wave function at a particular point has no physical meaning, and its value can be assigned arbitrarily; thus if we put
$$
\psi(x) \rightarrow \exp (-i b / \hbar) \psi(x)
$$
where $b$ is a free parameter with the dimensions of action, both wave functions describe the same physical state. Only the relative phase between two different space-time points is significant; more precisely we may assume that the relative phase is definite only if the two points are neighbouring [12]. In this framework one can repeat more or Iess verbatim Weyl’s argument described in $\$ 3.7 .1$ with the real vector in space-time replaced by the complex-valued wave function for the particle $\psi(x)$; the ramifications of this approach were described by Weyl in 1929 in a classic paper that showed how electromagnetism in quantum mechanics should be understood as a gauge theory [11].
In general $b$ can be taken to be a local function, $b=b(x)$, since the phase may vary with the position of the particle. Let us suppose that the phase of the wave function at a point has been chosen according to some specific calibration. A change in the phase of the wave function can be thought of as a unitary transformation, provided $b(x)$ satisfies appropriate (and fairly mild) analytical conditions,
$$
\psi(x) \rightarrow \psi(x)^{\prime}=\mathrm{U}_b \psi(x)
$$
with
$$
\mathrm{U}_b=\exp (-i b(x) / \hbar)
$$
In infinitesimal form the unitary transformation $(9.10)$ is
$$
\psi(x) \rightarrow \psi(x)^{\prime}=\left(1-\frac{i}{\hbar} b(x)\right) \psi(x)
$$

物理代写|电动力学代写electromagnetism代考|Quantum Electrodynamics

The full quantisation of the classical Hamiltonian formalism for electrodynamics described in Chapter 3 can be approached in several different ways, depending on how the classical second class constraint for the interacting system of charges and field,
$$
\Omega_2=\boldsymbol{\nabla} \cdot \boldsymbol{\pi}+\rho \approx 0,
$$
is dealt with, and on the choice of variables.

The classical gauge-invariant Hamiltonian (3.258) and its P.B. algebra (3.259) – (3.262) are interpreted in terms of Hilbert space operators, and the Maxwell equations for the field operators,
$$
\begin{array}{r}
\boldsymbol{\nabla} \cdot \mathbf{B}=0 \
\varepsilon_0 \boldsymbol{\nabla} \cdot \mathbf{E}=\rho,
\end{array}
$$
hold as initial conditions.
Classical variables such as $\boldsymbol{\pi}$ and $\rho$ are interpreted as Hilbert space operators, and physical states of the system, $\left{\Psi_k\right}$, are selected by the requirement that they are annihilated by $\Omega_2$; that is, a physical state must satisfy the relation
$$
(\boldsymbol{\nabla} \cdot \pi+\rho) \Psi_k=0
$$
In this case, canonical P.B.s are still valid, and so the corresponding quantum operators satisfy canonical commutation relations. The Hamiltonian operator is given by the canonical quantisation of Eq. (3.225).
The canonical P.B.s are redefined as Dirac brackets by the imposition of a gauge condition for the vector potential so that $\Omega_2=0$ is valid as an ordinary equation (one of the Maxwell equations). The reduced Hamiltonian and the Dirac brackets given by (3.254)-(3.257) are then reinterpreted as operator relations on a Hilbert space that is fixed by the commutation relations for the chosen gauge.

Only the third possibility has been developed sufficiently for practical calculations involving atoms/molecules and radiation, simply because of the unique significance of the instantaneous Coulomb interaction when there is more than one charged particle.

电动力学代考

物理代写|电动力学代写electromagnetism代考|Wave Mechanics and Electromagnetism

作为介绍，我们根据波力学考虑粒子在外部经典电磁场中的情况。坐标表示中粒子的波函数 $\psi(x)$ 是时空坐标的复值函数， $x=(\mathbf{r}, t)$. 波函数在某一特定点的相位没有物理意义，其值可以任意指定；因此，如果涐们把
$$
\psi(x) \rightarrow \exp (-i b / \hbar) \psi(x)
$$
在哪里 $b$ 是具有作用维度的自由参数，两个波函数描述相同的物理状态。只有两个不同时空点之间的相对相位才有意义；更准确地说，我们可以假设只有当两点相邻时，相对相位才是确定的 [12]。在这个框架中，人们可以或多或少地逐字重复 Weyl 在 $\$ 3.7 .1$ 用粒子的复值波函数代替时空中的实向量 $\psi(x)$ ；Weyl 在 1929 年的一篇经典论文中描述了这种方法的后果，该论文展示了如何将量子力学中的电磁学理解为规范理论 [11]。
一般来说 $b$ 可以看作是局部函数， $b=b(x)$ ，因为相位可能随粒子的位置而变化。让我们假设波函数在某一点的相位是根据某种特定的校准来选择的。波函数相位的变化可以被认为是酉变换，前提是 $b(x)$ 满足适当（且相当温和）的分析条件，
$$
\psi(x) \rightarrow \psi(x)^{\prime}=\mathrm{U}_b \psi(x)
$$
和
$$
\mathrm{U}_b=\exp (-i b(x) / \hbar)
$$
无穷小形式的酉变换 $(9.10)$ 是
$$
\psi(x) \rightarrow \psi(x)^{\prime}=\left(1-\frac{i}{\hbar} b(x)\right) \psi(x)
$$

物理代写|电动力学代写electromagnetism代考|Quantum Electrodynamics

第 3 章中描述的电动力学经典哈密顿形式的完全量化可以通过几种不同的方式来实现，这取决于电荷和场相互作用系统的经典二等约束，
$$
\Omega_2=\boldsymbol{\nabla} \cdot \boldsymbol{\pi}+\rho \approx 0
$$
处理，以及变量的选择。

经典规范不变哈密顿量 (3.258) 及其 PB 代数 (3.259) – (3.262) 根据莃尔伯特空间算子和场算子的麦克斯韦方程来解释，
$$
\boldsymbol{\nabla} \cdot \mathbf{B}=0 \varepsilon_0 \boldsymbol{\nabla} \cdot \mathbf{E}=\rho
$$
保持为初始条件。求选择 $\Omega_2 ;$ 也就是说，物理状态必须满足关系
$$
(\boldsymbol{\nabla} \cdot \pi+\rho) \Psi_k=0
$$
在这种情况下，规范 PB 仍然有效，因此相应的量子算符满足规范对换关系。哈密顿算子由等式的规范量化给出。(3.225)。
通过对矢量势施加规范条件，将规范 $P B$ 重新定义为狄拉克括号，以便 $\Omega_2=0$ 作为普通方程（麦克斯韦方程之一) 有效。由 (3.254)-(3.257) 给出的简化哈密顿量和狄拉克括号然后被重新解释为㳍尔伯特空间上的算子关系，该空间由所选规范的交换关系固定。
对于涉及原子/分子和辐射的实际计算，只有第三种可能性得到充分发展，这仅仅是因为当存在多个带电粒子时瞬时库仑相互作用的独特意义。

物理代写|电动力学代写electromagnetism代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

物理代写|电动力学代写electromagnetism代考|PHYS3040

Posted on 2023年3月29日2023年3月29日 by statistics-lab

如果你也在怎样代写电动力学electrodynamics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

电动力学是物理学的一个分支，处理快速变化的电场和磁场。

我们提供的电动力学electrodynamics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

物理代写|电动力学代写electromagnetism代考|Quantum Chemistry and the Coulomb Hamiltonian

There are various approaches to the solution of the molecular Schrödinger equation in the quantum chemistry/chemical physics literature starting from the Coulomb Hamiltonian. Firstly, the functions in (8.143) can be used as the basis of a Rayleigh-Ritz calculation being, hopefully, well-adapted to the construction of appropriate trial functions. Several different lines have been developed; in the adiabatic model the trial function is written as the continuous linear superposition
$$
\begin{aligned}
\Psi\left(\mathbf{t}^{\mathrm{e}}, \mathbf{t}^{\mathrm{n}}\right)m & =\int F(\mathbf{b}) \varphi\left(\mathbf{b}, \mathbf{t}^{\mathrm{c}}\right)_m \delta\left(\mathbf{t}^{\mathrm{n}}-\mathbf{b}\right) \mathrm{d} \mathbf{b} \ & =F\left(\mathbf{t}^{\mathrm{n}}\right) \varphi\left(\mathbf{t}^{\mathrm{n}}, \mathbf{t}^{\mathrm{c}}\right)_m, \end{aligned} $$ where the square integrable weight factor $F\left(\mathbf{t}^{\mathrm{n}}\right)$ may be determined by reducing (8.129) to an effective Schrödinger equation for the nuclei in which $F\left(\mathbf{t}^{\mathrm{n}}\right)$ appears as the eigenfunction [72]. Since the $\left{\varphi_m\right}$ are orthonormal we have $$ \left\langle\Psi_m \mid \Psi_m\right\rangle=\iint\left|\Psi\left(\mathbf{t}^{\mathrm{e}}, \mathbf{t}^{\mathrm{n}}\right)_m\right|^2 \mathrm{dt}^{\mathrm{e}} \mathrm{dt}^{\mathrm{n}}=\int\left|F\left(\mathbf{t}^{\mathrm{n}}\right)\right|^2 \mathrm{dt}^{\mathrm{n}} . $$ On the other hand the $(\mathrm{mm})$ matrix element of the translationally invariant Hamiltonian $\mathrm{H}^{\prime}$ can be written as $$ \left\langle\Psi_m\left|\mathrm{H}^{\prime}\right| \Psi_m\right\rangle=\iint \Psi_m^\left(\mathrm{H}^{\prime} \Psi_m\right) \mathrm{dt}^{\mathrm{e}} \mathrm{dt}^{\mathrm{n}}=\int F\left(\mathbf{t}^{\mathrm{n}}\right)^\left(\mathrm{H}_m F\right)\left(\mathbf{t}^{\mathrm{n}}\right) \mathrm{dt} \mathbf{t}^{\mathrm{n}}
$$
where we have defined the effective nuclear Hamiltonian,
$$
\left(\mathrm{H}_m F\right)\left(\mathbf{t}^{\mathrm{n}}\right)=\int \varphi\left(\mathbf{t}^{\mathrm{e}}, \mathbf{t}^{\mathrm{n}}\right)_m\left[\mathrm{H}^{\prime} \varphi\left(\mathbf{t}^{\mathrm{e}}, \mathbf{t}^{\mathrm{n}}\right)_m F\left(\mathbf{t}^{\mathrm{n}}\right)\right] \mathrm{d}^{\mathrm{e}} .
$$
The Rayleigh-Ritz quotient,
$$
E\left[\Psi_m\right]=\frac{\left\langle\Psi_m\left|H^{\prime}\right| \Psi_m\right\rangle}{\left\langle\Psi_m \mid \Psi_m\right\rangle}
$$
is stationary for those functions that are solutions of the effective nuclear ‘Schrödinger equation’,
$$
\mathrm{H}_m F_s=E{m s} F_s
$$
In particular, using the ground electronic state $\varphi_0$, the Rayleigh-Ritz quotient leads to an upper bound to the ground state energy $E_0$ of $\mathrm{H}^{\prime}$. This calculation amounts to the diagonalisation of $\mathrm{H}^{\prime}$ in the one-dimensional subspace spanned by $\Psi_0$. The subspace may be enlarged, and the accuracy thereby improved, by using the subspace spanned by a set of trial functions $\left(\Psi_0, \Psi_1, \cdots, \Psi_m\right)$ of the form of (8.162). So far no symmetries of the Coulomb Hamiltonian have been discarded.

物理代写|电动力学代写electromagnetism代考|The Quantisation of Electrodynamics

Rather than proceeding directly to quantum electrodynamics (QED), it may be helpful to summarise first the actual historical development since this still exerts a powerful influence on the way the theory of the interaction of electromagnetic radiation with matter in the ‘non-relativistic’ (low-energy) regime is presented. The return to electrodynamics that followed the success of quantum mechanics in accounting for the stability of atoms in terms of electrostatic forces was based on a very different conception from the earlier classical one; henceforth the electromagnetic field was to be treated as a weak perturbation of the atomic states, and so the concept of an isolated atom became a central feature of the new mechanics. The pathologies due to self interaction (‘radiation reaction’) that had plagued classical electrodynamics were put to one side with the assumption that one could use the experimental charge and mass parameters of the electron and the atomic nucleus. By treating the electromagnetic field as an external, classical perturbation of an atom, Schrödinger was able to calculate the Einstein $B$-coefficient for stimulated absorption and emission, and the cross section for linear light scattering [1] which turned out to be equivalent to the formula obtained earlier by Kramers and Heisenberg using the correspondence principle. These calculations were the prototypes for what has become known as the semiclassical radiation model which we shall describe in modern terms in 89.5 .

Shortly afterwards, quantum electrodynamics for the atom-radiation system was developed by Dirac, who discovered the boson quantisation of the free radiation field and used it to represent the Coulomb gauge vector potential as a quantum mechanical operator [2]. Dirac was able to reproduce Schrödinger’s results for stimulated absorption and emission and linear light scattering, but he also calculated directly Einstein’s A-coefficient for spontaneous emission. A particularly important result of Dirac’s calculation is that the relationship between the $A$ – and $B$-coefficients for a transition at frequency $\omega$,
$$
A=\frac{\hbar \omega^3}{\pi^2 c^3} B
$$
is quite general and is not limited to radiation in thermal equilibrium with its surroundings as originally assumed by Einstein [3]. On the other hand it quickly became apparent that the ugly pathologies due to self-interaction would also have to be revisited in the quantum mechanical theory [4], [5].

In this chapter we shall discuss some general features of both classical and quantum mechanical descriptions of the electromagnetic field, paying particular attention to the freedom to make gauge transformations of the field potentials, and sketch briefly a few ideas about the relationship of the semiclassical model to QED. Within the perturbation approach the question of the stability of atoms and molecules is no longer a question for $\mathrm{QED}$, as it had been for classical physics, and so an extensive quantum theory of atoms and molecules has developed over many years in which electromagnetic radiation plays only the subsidiary role of causing transitions between their states in absorption, emission and scattering processes. This is the case for both classical and quantum mechanical descriptions of the electromagnetic field. The ground state of an atom $^1$ cannot decay through the spontaneous emission mechanism, and so its stability is not in question in the perturbation theory framework. More recently the existence of a stable ground state for an atom and the fate of Bohr’s excited ‘stationary states’ in the presence of the quantised radiation field has been considered in a non-perturbative framework using the methods of functional analysis; we shall take this up in Chapter 11.

电动力学代考

物理代写|电动力学代写electromagnetism代考|Quantum Chemistry and the Coulomb Hamiltonian

从库仑哈密顿量开始，在量子化学/化学物理文献中有多种求解分子薛定谔方程的方法。首先，(8.143) 中的函数可以用作 Rayleigh-Ritz 计算的基础，希望能够很好地适应适当试验函数的构造。已经开发了几种不同的产品线；在绝热模型中，试验函数写为连续线性㖵加
$$
\Psi\left(\mathbf{t}^{\mathrm{e}}, \mathbf{t}^{\mathrm{n}}\right) m=\int F(\mathbf{b}) \varphi\left(\mathbf{b}, \mathbf{t}^{\mathrm{c}}\right)_m \delta\left(\mathbf{t}^{\mathrm{n}}-\mathbf{b}\right) \mathrm{d} \mathbf{b} \quad=F\left(\mathbf{t}^{\mathrm{n}}\right) \varphi\left(\mathbf{t}^{\mathrm{n}}, \mathbf{t}^{\mathrm{c}}\right)_m,
$$
其中平方可积权重因子 $F\left(\mathrm{t}^{\mathrm{n}}\right)$ 可以通过将 (8.129) 简化为原子核的有效辡定谔方程来确定，其中 $F\left(\mathrm{t}^{\mathrm{n}}\right)$ 表现为本征函数 [72]。自从佐{{|varphi_m|右} 是正交的，我们有
$$
\left\langle\Psi_m \mid \Psi_m\right\rangle=\iint\left|\Psi\left(\mathbf{t}^{\mathrm{e}}, \mathbf{t}^{\mathrm{n}}\right)_m\right|^2 \mathrm{dt}^{\mathrm{e}} \mathrm{dt}^{\mathrm{n}}=\int\left|F\left(\mathbf{t}^{\mathrm{n}}\right)\right|^2 \mathrm{dt}^{\mathrm{n}} .
$$
另一方面 $(\mathrm{mm})$ 平移不变哈密顿量的矩阵元素 $\mathrm{H}^{\prime}$ 可以写成
$$
\left\langle\Psi_m\left|\mathrm{H}^{\prime}\right| \Psi_m\right\rangle=\iint \Psi_m^{\left(\mathrm{H}^{\prime} \Psi_m\right)} \mathrm{dt}^{\mathrm{e}} \mathrm{dt}^{\mathrm{n}}=\int F\left(\mathbf{t}^{\mathrm{n}}\right)^{\left(\mathrm{H}_m F\right)}\left(\mathbf{t}^{\mathrm{n}}\right) \mathrm{dtt}^{\mathrm{n}}
$$
我们在这里定义了有效的核哈密顿量，
$$
\left(\mathrm{H}_m F\right)\left(\mathbf{t}^{\mathrm{n}}\right)=\int \varphi\left(\mathbf{t}^{\mathrm{e}}, \mathbf{t}^{\mathrm{n}}\right)_m\left[\mathrm{H}^{\prime} \varphi\left(\mathbf{t}^{\mathrm{e}}, \mathbf{t}^{\mathrm{n}}\right)_m F\left(\mathbf{t}^{\mathrm{n}}\right)\right] \mathrm{d}^{\mathrm{e}} .
$$
瑞利-里兹商数，
$$
E\left[\Psi_m\right]=\frac{\left\langle\Psi_m\left|H^{\prime}\right| \Psi_m\right\rangle}{\left\langle\Psi_m \mid \Psi_m\right\rangle}
$$
对于那些作为有效核“辡定谔方程”的解的函数是固定的，
$$
\mathrm{H}_m F_s=E m s F_s
$$
特别是，使用地面电子状态 $\varphi_0$ ，Rayleigh-Ritz 商导致基态能量的上限 $E_0$ 的 $\mathrm{H}^{\prime}$. 该计算相当于对角化 $\mathrm{H}^{\prime}$ 在跨越的一维子空间中 $\Psi_0$. 通过使用由一组试验函数跨越的子空间，可以扩大子空间，从而提高精度 $\left(\Psi_0, \Psi_1, \cdots, \Psi_m\right)$ 的形式 (8.162)。到目前为止，没有库仑哈密顿量的对称性被丟弃。

物理代写|电动力学代写electromagnetism代考|The Quantisation of Electrodynamics

与其直接进行量子电动力学 (QED)，不如首先总结实际的历史发展可能会有所帮助，因为这仍然对“非相对论”中电磁辐射与物质相互作用的理论产生强大影响 (低能量) 制度提出。随着量子力学成功地用静电力解释原子的稳定性，电动力学的回归基于与早期经典概念截然不同的概念；从此以后，电磁场被视为原子态的微弱扰动，因此孤立原子的概念成为新力学的核心特征。由于假设人们可以使用电子和原子核的实验电荷和质量参数，困扰经典电动力学的自相互作用 (“辐射反应”) 引起的病态被放在一边。通过将电磁场视为原子的外部经典扰动，薛定谔能够计算出爱因斯坦 $B$ – 受激吸收和发射的系数，以及线性光散射的横截面 [1] 结果证明等同于 Kramers 和 Heisenberg 先前使用对应原理获得的公式。这些计算是我们将在 89.5 中用现代术语描述的半经典辐射模型的原型。
不久之后，狄拉克开发了原子辐射系统的量子电动力学，他发现了自由辐射场的玻色子量子化，并用它来表示库仑规范矢量势作为量子力学算符 [2]。狄拉克能够重现薛定谔关于受激吸收和发射以及线性光散射的结果，但他也直接计算了爱因斯坦的自发辐射 $\mathrm{A}$ 系数。狄拉克计算的一个特别重要的结果是 $A$-和 $B$-频率转换的系数 $\omega$ ，
$$
A=\frac{\hbar \omega^3}{\pi^2 c^3} B
$$
是非常普遍的，并不局限于爱因斯坦最初假设的与周围环境处于热平衡状态的辐射 [3]。另一方面，很快就很明显，由于自相互作用而导致的丑陃病态也必须在量子力学理论中重新审视 [4]，[5]。
在本章中，我们将讨论电磁场的经典和量子力学描述的一些一般特征，特别注意对场势进行规范变换的自由度，并简要概述半经典模型与电磁场之间关系的一些想法QED。在微扰方法中，原子和分子的稳定性问题不再是一个问题 $\mathrm{QED}$ ，就像经典物理学一样，因此多年来发展了一种广泛的原子和分子量子理论，其中电磁辐射仅在吸收、发射和散射过程中引起状态之间的跃迁起辅助作用。电磁场的经典和量子力学描述都是这种情况。原子的基态 ${ }^1$ 不能通过自发辐射机制衰减，因此其稳定性在微扰理论框架中不成问题。最近，使用泛函分析方法在非微扰框架中考虑了原子稳定基态的存在以及存在量子化辐射场时玻尔激发的 “稳态”的命运；我们将在第 11 章讨论这个问题。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

物理代写|固体物理代写Solid-state physics代考|PHYSICS7544

Posted on 2023年3月29日2023年3月29日 by statistics-lab

如果你也在怎样代写固体物理Solid-state physics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

固态物理学是通过量子力学、晶体学、电磁学和冶金学等方法研究刚性物质或固体。它是凝聚态物理学的最大分支。

statistics-lab™ 为您的留学生涯保驾护航在代写固体物理Solid-state physics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写固体物理Solid-state physics代写方面经验极为丰富，各种代写固体物理Solid-state physics相关的作业也就用不着说。

我们提供的固体物理Solid-state physics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

物理代写|固体物理代写Solid-state physics代考|PHYSICS7544

物理代写|固体物理代写Solid-state physics代考|Quantum Numbers for the Hydrogen Atom Wave Function

In the process of solving the Schrödinger wave equation for hydrogen like atoms, the integer $\mathrm{n}, l$ and $\mathrm{m}$ are introduced in a logical way. These integers are called quantum numbers. In Bohr’s theory the quantum number $n$ is introduced arbitrarily in the form of the quantized condition. The wave function $\Psi_{\operatorname{nlm}}(\theta, \varphi)$ is description of states of the system. They are related to $n, l$ and $m$. Thus the quantum number themselves may be said to describe the state of the system. The values of these quantum numbers are
$$
\begin{aligned}
n & =1,2,3, \ldots \
l & =0,1,2, \ldots, n-1 \
m & =0, \pm 1, \pm 2, \ldots, \pm l
\end{aligned}
$$
It is now shown that the quantum numbers $l$ and $m$ are related to the magnitude $L$ of the orbital angular momentum and $m$ is the $z$ component $L_z . Y_{l m}(\theta, \varphi)$ is simultaneously the eigenfunction of $L^2$ and $L_z$ operator. Therefore, $L^2$ and $L_z$ commute, i.e. corresponding observable can be precisely measured simultaneously. The magnitude of the orbital angular momentum is $\hbar \sqrt{l(l+1)}$ while that of $L_z$ is $m \mathrm{~h}$. Since $L^2$ and $L_z$ do not operate on the radial part of the wave function, $\Psi_{n l m}(\theta, \varphi)$ itself is a simultaneous eigenfunction of $L^2$ and $L_z$. The quantum number $l$ gives the magnitude of the angular momentum, $m$ the orientation of the angular momentum and $\mathrm{n}$ gives the quantization of energy. The quantum numbers $l$ and $m$ can be equal only for $l=0$.

物理代写|固体物理代写Solid-state physics代考|Harmonic Oscillator

The harmonic oscillator is a system in which a particle of mass $m$ subject to a linear restoring force $\mathbf{F}$ proportional to the displacement $x$ from the equilibrium position
$$
F=-k x
$$
The proportionality constant $k$ is known as force constant. The minus sign indicates that force is in the direction opposite to the direction of the displacement.
The potential energy is given by
$$
\begin{gathered}
V=\frac{1}{2} k x^2=\frac{1}{2} m \omega^2 x^2 \
\omega=\sqrt{\frac{k}{m}}
\end{gathered}
$$
One Dimensional Harmonic Oscillator
The Schrödinger wave equation in one dimension for a particle of mass $m$ is
$$
\frac{\mathrm{d}^2 \psi}{\mathrm{d} x^2}+\frac{2 m}{\hbar^2}[E-V] \psi=0
$$ where $E$ is the energy and $V$ is given by Eq. (4.124). Substituting the value of $V$ in Eq. $(4.126)$
$$
\frac{\mathrm{d}^2 \psi}{\mathrm{d} x^2}+\frac{2 m}{\hbar^2}\left[E-\frac{1}{2} k x^2\right] \psi=0
$$
Let
$$
\begin{gathered}
\lambda=\frac{2 m}{\hbar^2} E \
\alpha^2=\frac{m k}{\hbar^2}=\frac{m^2 \omega^2}{\hbar^2}
\end{gathered}
$$
Equation (4.127) is then written as
$$
\frac{d^2 \psi}{d x^2}+\left(\lambda^2-\alpha^2 x^2\right) \psi=0
$$
with the boundary condition $\psi \rightarrow 0$ as $|x| \rightarrow \infty$. Let us suppose $\alpha x$ to be very large in particular $\alpha x>>1$ and $\alpha x \gg \lambda$.

固体物理代写

物理代写|固体物理代写Solid-state physics代考|Quantum Numbers for the Hydrogen Atom Wave Function

在求解类氢原子薛定谔波动方程的过程中，整数 $\mathrm{n}, l$ 和 $\mathrm{m}$ 以合乎逻辑的方式介绍。这些整数称为量子数。在玻尔的理论中，量子数 $n$ 以量化条件的形式任意引入。波函数 $\Psi_{\mathrm{nlm}}(\theta, \varphi)$ 是系统状态的描述。它们与 $n, l$ 和 $m$. 因此，可以说量子数本身描述了系统的状态。这些量子数的值是
$$
n=1,2,3, \ldots l=0,1,2, \ldots, n-1 m=0, \pm 1, \pm 2, \ldots, \pm l
$$
现在证明量子数l和 $m$ 与幅度有关 $L$ 轨道角动量和 $m$ 是个 $z$ 成分 $L_z . Y_{l m}(\theta, \varphi)$ 同时是的特征函数 $L^2$ 和 $L_z$ 操作员。所以， $L^2$ 和 $L_z$ 通勤，即可以同时精确测量相应的可观察值。轨道角动量的大小是 $\hbar \sqrt{l(l+1)}$ 而那个 $L_z$ 是 $m \mathrm{~h}$. 自从 $L^2$ 和 $L_z$ 不对波函数的径向部分进行操作， $\Psi_{n l m}(\theta, \varphi)$ 本身是同时的特征函数 $L^2$ 和 $L_z$. 量子数 $l$ 给出角动量的大小， $m$ 角动量的方向和 $\mathrm{n}$ 给出能量的量子化。量子数 $l$ 和 $m$ 只能等于 $l=0$.

物理代写|固体物理代写Solid-state physics代考|Harmonic Oscillator

谐振子是一个系统，其中一个质量粒子 $m$ 受到线性恢复力 $\mathbf{F}$ 与位移成正比 $x$ 从平衡位置
$$
F=-k x
$$
比例常数 $k$ 被称为力常数。负号表示力的方向与位移的方向相反。势能由下式给出
$$
V=\frac{1}{2} k x^2=\frac{1}{2} m \omega^2 x^2 \omega=\sqrt{\frac{k}{m}}
$$
一维谐振子质量
粒子的一维薛定谔波动方程 $m$ 是
$$
\frac{\mathrm{d}^2 \psi}{\mathrm{d} x^2}+\frac{2 m}{\hbar^2}[E-V] \psi=0
$$
在哪里 $E$ 是能量和 $V$ 由方程式给出。(4.124)。代入价值 $V$ 在等式中 (4.126)
$$
\frac{\mathrm{d}^2 \psi}{\mathrm{d} x^2}+\frac{2 m}{\hbar^2}\left[E-\frac{1}{2} k x^2\right] \psi=0
$$
让
$$
\lambda=\frac{2 m}{\hbar^2} E \alpha^2=\frac{m k}{\hbar^2}=\frac{m^2 \omega^2}{\hbar^2}
$$
方程 (4.127) 可以写成
$$
\frac{d^2 \psi}{d x^2}+\left(\lambda^2-\alpha^2 x^2\right) \psi=0
$$
与边界条件 $\psi \rightarrow 0$ 作为 $|x| \rightarrow \infty$. 让我们假设 $\alpha x$ 特别是非常大 $\alpha x>>1$ 和 $\alpha x \gg \lambda$.

物理代写|固体物理代写Solid-state physics代考| 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

物理代写|固体物理代写Solid-state physics代考|PHYSICS3544

Posted on 2023年3月29日2023年3月29日 by statistics-lab

如果你也在怎样代写固体物理Solid-state physics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

固态物理学是通过量子力学、晶体学、电磁学和冶金学等方法研究刚性物质或固体。它是凝聚态物理学的最大分支。

我们提供的固体物理Solid-state physics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

物理代写|固体物理代写Solid-state physics代考|PHYSICS3544

物理代写|固体物理代写Solid-state physics代考|Boundary Conditions

The wave function itself has no physical interpretation, however, the square of its absolute magnitude $|\Psi(x, t)|^2$ evaluated at a particular place and at a particular time is proportional to the possibility of finding the particle at that time. The probability density $|\Psi(x, t)|^2$ is positive and real and is taken equal to $\Psi^*(\boldsymbol{r}, t) \Psi(\boldsymbol{r}, t)$. The wave function $\Psi$ can take on negative values but probability density is always be positive. Besides fulfilling the normalization condition a solution of the time independent Schrödinger equation must obey the following boundary conditions.

The wave function must be continuous and single valued.
$\frac{\partial \psi}{\partial x}, \frac{\partial \psi}{\partial y}$ and $\frac{\partial \psi}{\partial z}$ must be continuous and single valued everywhere.
The integral of the square modulus of the wave function over all values $x$ must be finite
$$
\int \psi^* \psi \mathrm{d} \tau=\text { finite }
$$
that is the wave function must be square integrable. This condition means that wave function must be normalizable that is wave function must go to zero as $x(y, z) \rightarrow \pm \infty$ in order that $\int|\Psi|^2 \mathrm{~d} \tau$ over all space is finite constant.

The boundary conditions ensure that the probability of finding the particle in the vicinity of any point is unambiguously defined rather than having two or more possible values. Thus the wave function is single valued and continuous. If $\psi(x)$ and $(\mathrm{d} \psi / \mathrm{d} x)$ are not single valued, finite then the same is true for $\Psi(x, t)$. Since the given formula for calculating the expectation values of position and momentum contains $\Psi(x, t)$ and $\frac{\partial \Psi}{\partial t}$. We observe that in any of these cases we might not obtain finite and definite values when we evaluate measured quantities.

The first derivative of the wave function with respect to position coordinates must be continuous every where except where there is an infinite discontinuity in the potential. We know any function always has an infinite derivative whenever it has a discontinuity. Let us consider the time independent Schrödinger Eq. (4.67) in one dimension
$$
\frac{\mathrm{d}^2 \Psi}{\mathrm{d} x^2}=\frac{2 m}{\hbar^2}(V-E) \psi
$$
for finite $V, E$ and $\psi,\left(\mathrm{d}^2 \psi / \mathrm{d} x^2\right)$ is finite. This in turn requires (d $\psi / \mathrm{d} x$ ) to be continuous. A finite discontinuity in $(\mathrm{d} \psi / \mathrm{d} x)$ implies an infinite discontinuity in $\left(\mathrm{d}^2 \psi / \mathrm{d} x^2\right)$ and from the Schrödinger equation in $V(x)$.

物理代写|固体物理代写Solid-state physics代考|Hydrogen Atom

Consider the hydrogen atom as a system of two interacting particles, the interaction being due to Coulomb attraction of their electrical charges. Let the charge on the nucleus is $Z q$ and the charge on the electron is $-q$. The potential energy of the system in the absence of the external field is
$$
V(r)=-\frac{Z q^2}{\left(4 \pi \varepsilon_0\right) r}
$$
in which $r$ is the distance between the electron and the nucleus.
Let $m_1$ and $m_2$ are the masses of nucleus and the electron, respectively. If we write for the Cartesian coordinates of the nucleus and the electrons $x_1, y_1, z_1$ and $x_2, y_2, z_2$, respectively, the Hamiltonian of the hydrogenic atoms has the form
$$
H=\frac{p_1^2}{2 m_1}+\frac{p_2^2}{2 m_2}+V(r)=E
$$
The Schrödinger wave equation is $$
\frac{1}{m_1}\left(\frac{\partial^2 \Psi}{\partial x_1^2}+\frac{\partial^2 \Psi}{\partial y_1^2}+\frac{\partial^2 \Psi}{\partial z_1^2}\right)+\frac{1}{m_2}\left(\frac{\partial^2 \Psi}{\partial x_2^2}+\frac{\partial^2 \Psi}{\partial y_2^2}+\frac{\partial^2 \Psi}{\partial z_2^2}\right)+\frac{2}{\hbar^2}[E-V] \Psi=0
$$
Here wave function $\Psi$ refers to the complete system with six coordinates. Equation (4.73) can be separated into two, one of which represents the translational motion of a molecule as a whole and the other, the relative motion of the two particles. For this, consider new variables $X, Y, Z$ which are Cartesian coordinates of the centre of mass of the system and $r, \theta$ and $\varphi$ of the polar coordinates of the second particle relative to the first. These coordinates are related to the Cartesian coordinates of the two particles by the equations
$$
\begin{gathered}
X=\frac{m_1 x_1+m_2 x_2}{m_1+m_2} \
Y=\frac{m_1 y_1+m_2 y_2}{m_1+m_2} \
Z=\frac{m_1 z+m_2 z_2}{m_1+m_2} \
x=x_2-x_1=r \sin \theta \cos \varphi \
y=y_2-y_1=r \sin \theta \sin \varphi \
z=z_2-z_1=r \cos \theta
\end{gathered}
$$

固体物理代写

物理代写|固体物理代写Solid-state physics代考|Boundary Conditions

波函数本身没有物理解释，但是，它的绝对大小的平方 $|\Psi(x, t)|^2$ 在特定地点和特定时间评估的值与在该时间找到粒子的可能性成正比。概率密度 $|\Psi(x, t)|^2$ 是正实数，取等于 $\Psi^*(\boldsymbol{r}, t) \Psi(\boldsymbol{r}, t)$. 波函数 $\Psi$ 可以取负值，但概率密度始终为正。除了满足归一化条件外，与时间无关的薛定谔方程的解还必须遵守以下边界条件。

波函数必须是连续的和单值的。
$\frac{\partial \psi}{\partial x}, \frac{\partial \psi}{\partial y}$ 和 $\frac{\partial \psi}{\partial z}$ 必须是连续的并且处处都是单值的。
波函数的平方模对所有值的积分 $x$ 必须是有限的
$$
\int \psi^* \psi \mathrm{d} \tau=\text { finite }
$$
即波函数必须是平方可积的。这个条件意味着波函数必须是可归一化的，即波函数必须归零为 $x(y, z) \rightarrow \pm \infty$ 为了使 $\int|\Psi|^2 \mathrm{~d} \tau$ 在所有空间上都是有限常数。
边界条件确保在任何点附近找到粒子的概率被明确定义，而不是有两个或更多可能的值。因此波函数是单值连续的。如果 $\psi(x)$ 和 $(\mathrm{d} \psi / \mathrm{d} x)$ 不是单值的，有限的那么同样适用于 $\Psi(x, t)$. 由于用于计算位置和动量期望值的给定公式包含 $\Psi(x, t)$ 和 $\frac{\partial \Psi}{\partial t}$. 我们观察到，在任何这些情况下，当我们评估测量量时，我们可能无法获得有限和确定的值。
波函数相对于位置坐标的一阶导数在任何地方都必须是连续的，除了势能中存在无限不连续的地方。我们知道，任何函数只要有不连续点，就总是有无穷导数。让我们考虑时间无关的薛定谔方程。(4.67) 一维
$$
\frac{\mathrm{d}^2 \Psi}{\mathrm{d} x^2}=\frac{2 m}{\hbar^2}(V-E) \psi
$$
对于有限 $V, E$ 和 $\psi,\left(\mathrm{d}^2 \psi / \mathrm{d} x^2\right)$ 是有限的。这又需要 $(\mathrm{d} \psi / \mathrm{d} x)$ 是连续的。中的有限不连续性 $(\mathrm{d} \psi / \mathrm{d} x)$ 意味着无限不连续 $\left(\mathrm{d}^2 \psi / \mathrm{d} x^2\right)$ 从薛定谔方程 $V(x)$.

物理代写|固体物理代写Solid-state physics代考|Hydrogen Atom

将氢原子视为两个相互作用粒子的系统，相互作用是由于它们的电荷的库仑吸引。让原子核上的电荷是 $Z q$ 电子上的电荷是 $-q$. 在没有外场的情况下系统的势能是
$$
V(r)=-\frac{Z q^2}{\left(4 \pi \varepsilon_0\right) r}
$$
其中 $r$ 是电子与原子核之间的距离。
让 $m_1$ 和 $m_2$ 分别是原子核和电子的质量。如果我们写下原子核和电子的笛卡尔坐标 $x_1, y_1, z_1$ 和 $x_2, y_2, z_2$ ，氢原子的哈密顿量分别具有以下形式
$$
H=\frac{p_1^2}{2 m_1}+\frac{p_2^2}{2 m_2}+V(r)=E
$$
辠定谔波动方程是
$$
\frac{1}{m_1}\left(\frac{\partial^2 \Psi}{\partial x_1^2}+\frac{\partial^2 \Psi}{\partial y_1^2}+\frac{\partial^2 \Psi}{\partial z_1^2}\right)+\frac{1}{m_2}\left(\frac{\partial^2 \Psi}{\partial x_2^2}+\frac{\partial^2 \Psi}{\partial y_2^2}+\frac{\partial^2 \Psi}{\partial z_2^2}\right)+\frac{2}{\hbar^2}[E-V] \Psi=0
$$
这里的波函数 $\Psi$ 指具有六个坐标的完整系统。方程 (4.73) 可以分为两个，一个表示分子整体的平移运动，另一个表示两个粒子的相对运动。为此，考虑新变量 $X, Y, Z$ 这是系统质心的笛卡尔坐标和 $r, \theta$ 和 $\varphi$ 第二个粒子相对于第一个粒子的极坐标。这些坐标通过方程式与两个粒子的笛卡尔坐标相关
$$
X=\frac{m_1 x_1+m_2 x_2}{m_1+m_2} Y=\frac{m_1 y_1+m_2 y_2}{m_1+m_2} Z=\frac{m_1 z+m_2 z_2}{m_1+m_2} x=x_2-x_1=r \sin \theta \cos \varphi y=y_2
$$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|宏观经济学代写Macroeconomics代考|EC4505

Posted on 2023年3月28日2023年3月28日 by statistics-lab

如果你也在怎样代写宏观经济学Macroeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

宏观经济学，对国家或地区经济整体行为的研究。它关注的是了解整个经济的事件，如商品和服务的生产总量、失业水平和价格的一般行为。

statistics-lab™ 为您的留学生涯保驾护航在代写宏观经济学Macroeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写宏观经济学Macroeconomics代写方面经验极为丰富，各种代写宏观经济学Macroeconomics相关的作业也就用不着说。

我们提供的宏观经济学Macroeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

经济代写|宏观经济学代写Macroeconomics代考|The government budget constraint

Let us start by looking carefully at the government budget constraint. Let $g_t$ and $\tau_t$ denote the government’s real purchases and tax revenues at time $t$, and $d_0$, its initial real debt outstanding. The simplest definition of the budget deficit is that it is the rate of change of the stock of debt. The rate of change in the stock of real debt equals the difference between the government’s purchases and revenues, plus the real interest on its debt. That is,
$$
\dot{d}t=\left(g_t-\tau_t\right)+r d_t $$ where $r$ is the real interest rate. The term in parentheses on the right-hand side of (17.1) is referred to as the primary deficit. It is the deficit excluding interest payments of pre-existing debt, and it is often a better way of gauging how fiscal policy at a given time is contributing to the government’s budget constraint, since it leaves aside the effects of what was inherited from previous policies. The government is also constrained by the standard solvency (no-Ponzi game) condition $$ \lim {T \rightarrow \infty}\left(d_T e^{-r T}\right) \leq 0
$$

The government’s budget constraint does not prevent it from staying permanently in debt, or even from always increasing the amount of its debt. Recall that the household’s budget constraint in the Ramsey model implies that in the limit the present value of its wealth cannot be negative. Similarly, the restriction the budget constraint places on the government is that in the limit of the present value of its debt cannot be positive. In other words, the government cannot run a Ponzi scheme in which it raises new debt to pay for the ballooning interest on pre-existing debt. This condition is at the heart of the discussions on the solvency or sustainability of fiscal policy, and is the reason why sustainability exercises simply test that dynamics do not have government debt increase over time relative to GDP.
How do we impose this solvency condition on the government? We follow our standard procedure of solving the differential equation that captures the flow budget constraint. We can solve (17.1) by applying our familiar method of multiplying it by the integrating factor $e^{-r t}$, and integrating between 0 and $T$ :
$$
\begin{gathered}
\dot{d}t e^{-r t}-r d_t e^{-r t}=\left(g_t-\tau_t\right) e^{-r t} \Rightarrow \ d_T e^{-r T}=d_0+\int_0^T\left(g_t-\tau_t\right) e^{-r t} d t . \ \lim {T \rightarrow \infty}\left(d_T e^{-r T}\right)=d_0+\int_0^{\infty}\left(g_t-\tau_t\right) e^{-r t} d t \leq 0,
\end{gathered}
$$

经济代写|宏观经济学代写Macroeconomics代考|Ricardian equivalence

Let us now add households to the story, and ask questions about the effects of fiscal policy decisions on private actions and welfare. In particular, for a given path of spending, a government can choose to finance it with taxes or bonds. Does this choice make any difference? This question is actually at the heart of the issue of countercyclical fiscal policy. If you remember the standard Keynesian exercise, a fiscal stimulus is an increase in government spending that is not matched by an increase in current taxes. In other words, it is a debt-financed increase in spending. Is this any different from a policy that would raise taxes to finance the increased spending?

A natural starting point is the neoclassical growth model we have grown to know and love. To fix ideas, consider the case in which the economy is small and open, domestic agents have access to an international bond $b$ which pays an interest rate $r$ (the same as the interest rate on domestic government debt), and in which all government debt is held by domestic residents.

When there are taxes, the representative household’s budget constraint is that the present value of its consumption cannot exceed its initial wealth plus the present value of its after-tax labour income:
$$
\int_0^{\infty} c_t e^{-r t} d t=b_0+d_0+\int_0^{\infty}\left(y_t-\tau_t\right) e^{-r t} d t
$$
Notice that initial wealth now apparently has two components: international bond-holdings $b_0$ and domestic public debt holdings $d_0$.

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|The government budget constraint

让我们从仔细研究政府预算约束开始。让 $g_t$ 和 $\tau_t$ 表示政府当时的实际购买和税收收入 $t$ ，和 $d_0$ ，其初始实际末偿债务。预算赤字最简单的定义是债务存量的变化率。实际债务存量的变化率等于政府购买和收入之间的差额加上其债务的实际利息。那是，
$$
\dot{d} t=\left(g_t-\tau_t\right)+r d_t
$$
在哪里 $r$ 是实际利率。(17.1) 右侧括号中的术语称为主要赤字。它是不包括现有债务利息支付的赤字，它通常是衡量特定时期财政政策如何影响政府预算约束的更好方法，因为它忽略了从以前的政策中继承下来的影响. 政府也受到标准偿付能力（非庞氏游戏) 条件的约束
$$
\lim T \rightarrow \infty\left(d_T e^{-r T}\right) \leq 0
$$
政府的预算约束并不能阻止它永远负债侽侽，甚至不能阻止它不断增加债务数额。回想一下，Ramsey 模型中的家庭预算约束意味着，在极限情况下，其财富的现值不能为负。同样，预算约束对政府的限制是其债务的现值不能为正。换句话说，政府不能运行庞氏骗局，即筹集新债务来支付现有债务不断膨胀的利息。这种情况是关于财政政策的偿付能力或可持续性的讨论的核心，也是为什么可持续性练习只是测试动态不会让政府债务相对于 GDP 随时间增加的原因。
我们如何将这种偿付能力条件强加于政府? 我们遵循我们的标准程序来求解捕获流量预算约束的微分方程。我们可以通过应用我们熟悉的方法将它乘以积分因子来求解 $(17.1) e^{-r t}$ ，并在 0 和 $T$ :
$$
\dot{d} t e^{-r t}-r d_t e^{-r t}=\left(g_t-\tau_t\right) e^{-r t} \Rightarrow d_T e^{-r T}=d_0+\int_0^T\left(g_t-\tau_t\right) e^{-r t} d t . \lim T \rightarrow \infty\left(d_T e^{-r T}\right)
$$

经济代写|宏观经济学代写Macroeconomics代考|Ricardian equivalence

现在让我们将家庭添加到故事中，并提出有关财政政策决定对私人行为和福利的影响的问题。特别是，对于给定的支出路径，政府可以选择通过税收或债券为其融资。这个选择有什么区别吗? 这个问题实际上是反周期财政政策问题的核心。如果您还记得标准的凯恩斯主义练习，财政刺激就是增加政府支出，但不增加现行税收。换句话说，这是一种债务融资的支出增长。这与提高税收以资助增加的支出的政策有什么不同吗?
一个自然的起点是我们已经逐渐了解和喜爱的新古典主义增长模式。为了修正想法，考虑经济规模小且开放的情况，国内代理人可以获得国际债券 $b$ 支付利息 $r$ (与国内政府债务利率相同），其中政府债务全部由国内居民持有。
当有税收时，代表性家庭的预算约束是其消费的现值不能超过其初始财富加上其税后劳动收入的现值:
$$
\int_0^{\infty} c_t e^{-r t} d t=b_0+d_0+\int_0^{\infty}\left(y_t-\tau_t\right) e^{-r t} d t
$$
请注意，初始财富现在显然有两个组成部分：国际债券持有量 $b_0$ 和国内公共债务持有量 $d_0$.

经济代写|宏观经济学代写Macroeconomics代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|宏观经济学代写Macroeconomics代考|ECON6002

Posted on 2023年3月28日2023年3月28日 by statistics-lab

如果你也在怎样代写宏观经济学Macroeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

宏观经济学，对国家或地区经济整体行为的研究。它关注的是了解整个经济的事件，如商品和服务的生产总量、失业水平和价格的一般行为。

我们提供的宏观经济学Macroeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

经济代写|宏观经济学代写Macroeconomics代考|Insider-outsider models of unemployment

The insider-outsider model also speaks of a dual labour market, but for different reasons. A standard model of a dual market occurs when governments impose a minimum wage above the equilibrium rate leaving some workers unemployed. Alternatively, in the formal market, unionised workers choose the wage jointly with the firm in a bargaining process. The key assumption is that the firm cannot hire outsiders before it has all insiders (e.g. union members) working, and insiders have little incentive to keep wages low so that outsiders can get a job. As a result the equilibrium wage is higher than the market-clearing wage.

In these dual labour market stories, we may want to ask what is going on in the labour market for outsiders. That, in fact, is a free market, so there should be full employment there. In fact, for most developing countries unemployment is not a big issue, though a privileged number of formal workers do have higher wages. In other words, for the insider-outsider story to generate high economy-wide unemployment, you need the economy to have a very small informal sector. Examples could be European countries or Southern African countries.

At any rate, to see the insider-outsider story in action as a model of unemployment, consider an economy where all workers are unionised so that aggregate labour demand faces a unique supplier of labour: the centralised union. In Figure 16.4 we show that, as with any monopolist, the price is driven above its equilibrium level, and at the optimal wage there is excess supply of labour (unemployment). Notice that if the demand for labour increases the solution is an increase in the wage and in employment, so the model delivers a procyclical wage.

The role of labour market regulations on the functioning of the labour market is a literature with strong predicament in Europe, where unionisation and labour regulation were more prevalent than, say, in the U.S. In fact, Europe showed historically a higher unemployment rate than the U.S., a phenomenon called Eurosclerosis.

The literature has produced a series of interesting contributions surrounding labour market rigidities. One debate, for example has do to with the role of firing costs on equilibrium unemployment. Increasing firing costs increases or decreases unemployment? It increases unemployment, some would claim because it makes hiring more costly. Others would claim it reduces unemployment because it makes firing more costly. Bentolila and Bertola (1990) calibrated these effects for European labour markets and found that firing costs actually decrease firing and reduce the equilibrium unemployment rate. The debate goes on.

经济代写|宏观经济学代写Macroeconomics代考|Unemployment and rural-urban migration

Inspired by the slums of Nairobi, which swelled even further as the nation developed, Harris and Todaro (1970) developed the concept that unemployment was a necessary buffer whenever there were dual labour markets. It is a specific version of the insider-outsider interpretation. According to Harris and Todaro, there is a subsistence wage (back in the countryside) $\left(w_s\right)$ that coexists with the possibility of a job in the formal sector $\left(w_f\right)$. For the market to be in equilibrium, expected wages had to be equalised, i.e.
$$
p w_f=w_s
$$
where $p$ is the probability of finding a job in the formal sector. How is $p$ determined? Assuming random draws from a distribution we can assume that
$$
p=\frac{E}{E+U}
$$
where $E$ stands for the total amount of people employed, and $U$ for the total unemployed. Solving for $U$, using (16.47) in (16.48) we obtain that
$$
U=E\left(\frac{w_f-w_s}{w_s}\right),
$$
i.e. the unemployment rate is a function of the wage differential.

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|Insider-outsider models of unemployment

局内人-局外人模型也谈到双重劳动力市场，但出于不同的原因。当政府强制实施高于均衡水平的最低工资而导致一些工人失业时，就会出现双元市场的标准模型。或者，在正规市场上，加入工会的工人在讨价还价过程中与公司共同选择工资。关键的假设是，在所有内部人员（例如工会成员）都工作之前，公司不能雇用外部人员，并且内部人员没有动力保持低工资以便外部人员可以找到工作。结果，均衡工资高于市场出清工资。

在这些双重劳动力市场的故事中，我们可能想问问局外人在劳动力市场上发生了什么。事实上，那是一个自由市场，所以那里应该有充分的就业。事实上，对于大多数发展中国家来说，失业并不是一个大问题，尽管有一定数量的特权正式工人确实有更高的工资。换句话说，要使内部人与外部人的故事在整个经济范围内产生高失业率，你需要经济中有一个非常小的非正规部门。例子可以是欧洲国家或南部非洲国家。

无论如何，要将内部人与外部人的故事视为失业模型，请考虑一个所有工人都加入工会的经济体，以便总劳动力需求面对一个独特的劳动力供应商：集中工会。在图 16.4 中，我们表明，与任何垄断者一样，价格被推高至其均衡水平之上，并且在最优工资时存在劳动力过剩供给（失业）。请注意，如果对劳动力的需求增加，解决方案是增加工资和就业，因此该模型提供顺周期工资。

劳动力市场监管对劳动力市场运作的作用是欧洲面临严重困境的文献，那里的工会化和劳工监管比美国更普遍事实上，欧洲历史上的失业率高于美国，一种称为欧洲硬化症的现象。

文献围绕劳动力市场刚性做出了一系列有趣的贡献。例如，一场辩论与解雇成本对均衡失业率的作用有关。增加解雇成本会增加还是减少失业率？它增加了失业率，有些人会声称，因为它使招聘成本更高。其他人会声称它降低了失业率，因为它使解雇成本更高。Bentolila 和 Bertola (1990) 校准了这些对欧洲劳动力市场的影响，发现解雇成本实际上减少了解雇并降低了均衡失业率。辩论还在继续。

经济代写|宏观经济学代写Macroeconomics代考|Unemployment and rural-urban migration

受到内罗毕盆民窟的启发，随着国家的发展，盆民窟进一步扩大，哈里斯和托达罗（Harris and Todaro， 1970) 提出了一个概念，即只要存在双重劳动力市场，失业就是一个必要的缓冲。它是局内人-同外人解释的特定版本。根据哈里斯和托达罗的说法，有维持生计的工资（回到农村） $\left(w_s\right)$ 与在正规部门工作的可能性并存 $\left(w_f\right)$. 为了使市场处于均衡状态，预期工资必须相等，即
$$
p w_f=w_s
$$
在哪里 $p$ 是在正规部门找到工作的概率。怎么 $p$ 决定? 假设从分布中随机抽取，我们可以假设
$$
p=\frac{E}{E+U}
$$
在哪里 $E$ 代表就业总人数，并且U对于总失业人员。求解 $U$ ，在 (16.48) 中使用 (16.47) 我们得到
$$
U=E\left(\frac{w_f-w_s}{w_s}\right),
$$
即失业率是工资差异的函数。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|微观经济学代写Microeconomics代考|PACC6007

Posted on 2023年3月28日2023年3月28日 by statistics-lab

如果你也在怎样代写微观经济学Microeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

微观经济学是研究稀缺性及其对资源的使用、商品和服务的生产、生产和福利的长期增长的影响，以及对社会至关重要的其他大量复杂问题的研究。

statistics-lab™ 为您的留学生涯保驾护航在代写微观经济学Microeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics相关的作业也就用不着说。

我们提供的微观经济学Microeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

经济代写|微观经济学代写Microeconomics代考|Oligopoly

In an oligopoly a few producers satisfy the demand of many consumers. Different to perfectly competitive markets or monopolies, these producers pay attention to the behavior of the other oligopolists. As such, strategies play an important role in oligopolies and game theory is the foremost tool to study the behavior. Quantity and price in an oligopoly will be somewhere between monopoly and perfect competition.

In many cases, economists study oligopolies with the help of game theory. Game theory analyzes strategic interactions between rational decision-makers with the help of mathematical models. Founding fathers of game theory were von Neumann and Morgenstern (1944). Nash (1951) defined an equilibrium solution to a noncooperative game which later became known as Nash equilibrium. This is a situation where no player can change his strategy without becoming worse off if all other players keep their strategy.

A simple form of an oligopoly is a duopoly, the competition between two producers. Cournot (1838) developed a solution to the problem implying that producer A chooses his output by assuming a fixed output from producer $B$ (and vice versa) without further adjustments. This provides a stable equilibrium at a level below monopoly price and above monopoly quantity. The behavior of the two producers can be described as a simultaneous competition for quantities.

In the Stackelberg model (1934), producer A would anticipate the move of B and factor this outcome into his strategy in order to increase his own profit (and decrease the profit of B). The total profit of both producers will be smaller than the profits in the Cournot model and the monopoly but higher than in perfectly competitive markets. We are looking in difference to the Cournot model at a sequential competition for quantities.

The market outcomes are often suboptimal from the point of view of the oligopolists; the solutions do not reach an equilibrium. They might in such cases be tempted to collude by fixing prices. While this happens in real life and also in construction, it is illegal.

Oligopolies make use of advertising. These activities increase the costs of the producers and they are called transaction costs. Oligopolists and others facing such transaction costs will have to consider these in addition to the rule $M R=M C$. They create a gap between buying and selling price reducing the market quantity (Hirshleifer and Hirshleifer 1998, p. 410).

Specific market conditions need to be looked at to find a solution for an oligopoly since there are otherwise infinite possibilities of strategic behaviors. It seems to be advisable to look at the construction market in detail before advancing the theory of oligopolies (Chapter 14). We will find that oligopolies play a negligible role in construction.

经济代写|微观经济学代写Microeconomics代考|Factor Supply of Households

Households need money in order to be able to purchase necessary and luxury goods. The only chance for the majority is to offer their labor in the labor market and to earn a wage. To this end, individuals and households make decisions how they use their time. Time is a limited resource as the day has invariably 24 hours. An individual can choose how much time to spend working $(W)$ and economists call the remaining part of the day leisure $(L)$ whether it is used for cleaning, cooking, learning, or relaxing. The less an individual works, the less money he has for consumption and the more time for other activities. Instead of a budget constraint, the individual faces now a time constraint. Instead of choosing between a number of different goods, we are now looking at the time preferences of the individual. As before, constraints and preferences determine the decision of the individual in the neoclassical model (Figure 7.2).

A person can theoretically work 24 hours, and this provides the $y$-intercept for the time constraint; it also can work 0 hours and spend all day on leisure ( $x$-intercept). This way we can construct the time constraint in Figure 7.2. The explanations for the construction of indifference lines and utility maximization in Section 3.3 on consumer behavior are also valid for time preferences and maximizing decisions on the use of time.

It should be clear that most people are not free to decide how many hours to work, but looking at a total work life, there certainly is some flexibility for many. Changes in preferences lead to different choices. In some Western countries, young engineers today value leisure more than the generations before them. In other words, they prefer spending time with family and friends. Figure 7.3 shows the different preferences and outcomes.

The daily income $(y)$ is the product of work hours $\left(h_{\mathrm{W}}\right)$ and wage, and if we consider theoretically 24 hours as the maximum available time, then the choice of leisure hours $\left(h_{\mathrm{L}}\right)$ influences this income:
$$
y=w \cdot h_{\mathrm{W}}=w\left(24-h_{\mathrm{L}}\right)
$$
Differentiating Eq. (7.1) for $h_{\mathrm{L}}$ gives:
$$
d y / d h_L=-w
$$
Thus, the income-leisure combination has a slope of $-w$. An increase in income due to a higher wage can shift the choice toward more leisure time (Figure 7.4). This depends, of course, on the shape of the preference curves, but it is one possible outcome.

微观经济学代考

经济代写|微观经济学代写Microeconomics代考|Oligopoly

在寡头垄断中，少数生产者满足许多消费者的需求。与完全竞争市场或垄断不同，这些生产者关注其他寡头的行为。因此，策略在寡头垄断中起着重要作用，博弈论是研究行为的最重要工具。寡头垄断中的数量和价格介于垄断和完全竞争之间。

在许多情况下，经济学家在博弈论的帮助下研究寡头垄断。博弈论借助数学模型分析理性决策者之间的战略互动。博弈论的奠基人是冯·诺依曼和摩根斯坦（1944 年）。Nash (1951) 定义了非合作博弈的均衡解，后来被称为纳什均衡。在这种情况下，如果所有其他玩家都保持他们的策略，则没有玩家可以在不变得更糟的情况下改变他的策略。

寡头垄断的一种简单形式是双头垄断，即两个生产者之间的竞争。古诺 (Cournot, 1838) 提出了一个问题的解决方案，即生产者 A 通过假设生产者的固定输出来选择他的输出乙（反之亦然）无需进一步调整。这在低于垄断价格和高于垄断数量的水平上提供了稳定的均衡。两家生产商的行为可以描述为同时进行数量竞争。

在 Stackelberg 模型（1934 年）中，生产商 A 会预期 B 的移动并将这一结果纳入其战略，以增加自己的利润（并减少 B 的利润）。两个生产者的总利润将小于古诺模型和垄断中的利润，但高于完全竞争市场中的利润。我们正在寻找与古诺模型在数量顺序竞争中的区别。

从寡头垄断者的角度来看，市场结果往往是次优的；解决方案没有达到平衡。在这种情况下，他们可能会试图通过固定价格来串通一气。虽然这种情况发生在现实生活和建筑中，但它是非法的。

寡头垄断利用广告。这些活动增加了生产者的成本，它们被称为交易成本。除了规则之外，寡头垄断者和其他面临此类交易成本的人将不得不考虑这些米R=米C. 他们在买卖价格之间制造差距，减少市场数量（Hirshleifer 和 Hirshleifer 1998，第 410 页）。

需要查看特定的市场条件以找到寡头垄断的解决方案，因为否则存在无限的战略行为可能性。在推进寡头垄断理论（第 14 章）之前，详细研究建筑市场似乎是明智的。我们会发现寡头垄断在建设中的作用微乎其微。

经济代写|微观经济学代写Microeconomics代考|Factor Supply of Households

家庭需要钱才能购买必需品和奢侈品。大多数人的唯一机会是在劳动力市场上提供劳动力并赚取工资。为此，个人和家庭决定如何使用他们的时间。时间是有限的资源，因为一天总是 24 小时。个人可以选择花多少时间工作 $(W)$ 经济学家称一天的剩余时间为休闲 $(L)$ 无论是用于清洁、亨饪、学习还是放松。一个人的工作越少，他用于消费的钱就越少，用于其他活动的时间就越多。个人现在面临的不是预算限制，而是时间限制。我们现在不是在许多不同的商品之间进行选择，而是关注个人的时间偏好。和以前一样，约束和偏好决定了新古典模型中个人的决策 (图 7.2)。
一个人理论上可以24小时工作，这提供了 $y$-拦截时间限制；它还可以工作0小时，整天休闲 ( $x$-截距) 。这样我们就可以构建图 7.2 中的时间约束。 3.3 节关于消费者行为的无差异线构造和效用最大化的解释也适用于时间偏好和时间使用最大化决策。
应该清楚的是，大多数人不能自由决定工作多少小时，但从总的工作时间来看，对许多人来说肯定有一定的灵活性。偏好的变化导致不同的选择。在一些西方国家，今天的年轻工程师比他们的前几代人更看重休闲。换句话说，他们更喜欢与家人和朋友共度时光。图 7.3 显示了不同的偏好和结果。
每天的收入 $(y)$ 是工作时间的产物 $\left(h_{\mathrm{W}}\right)$ 和工资，如果我们将理论上的 24 小时视为最大可用时间，那么休闲时间的选择 $\left(h_{\mathrm{L}}\right)$ 影响收入:
$$
y=w \cdot h_{\mathrm{W}}=w\left(24-h_{\mathrm{L}}\right)
$$
微分方程 (7.1) 对于 $h_{\mathrm{L}}$ 给出:
$$
d y / d h_L=-w
$$
因此，收入-休闲组合的斜率为 $-w$. 由于更高的工资而增加的收入可以将选择转向更多的闲暇时间 (图 7.4）。当然，这取决于偏好曲线的形状，但这是一种可能的结果。

经济代写|微观经济学代写Microeconomics代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

经济代写|微观经济学代写Microeconomics代考|ECON1101

Posted on 2023年3月28日2023年3月28日 by statistics-lab

如果你也在怎样代写微观经济学Microeconomics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

微观经济学是研究稀缺性及其对资源的使用、商品和服务的生产、生产和福利的长期增长的影响，以及对社会至关重要的其他大量复杂问题的研究。

我们提供的微观经济学Microeconomics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

经济代写|微观经济学代写Microeconomics代考|Monopolistic Competition

Monopolistic competition is the most prevalent market configuration besides heterogenous oligopolies. Under these conditions, producers offer differentiated products – and not homogenous goods – that serve the same purpose such as T-shirts, and consumers have preferences for certain products. This allows some space for producers to set prices. They are no longer price-takers but they also do not have the freedom of normal monopolists. Their market power is more limited. Producers can differentiate products mainly by style, location, or quality. The more a producer is able to differentiate the products, the stronger the market power. Each producer provides only a relatively small quantity of goods to the market so that its actions have no impact on other producers. Thus, if a producer raises the price of a product, it will lose some customers but not all, as under the conditions of perfect competition.

However, the producer is threatened by new firms who can enter the market and attack the differentiated product. The possibility of free market entry reduces profits to zero in the long run. This result is the same as for perfect competition, but other results are different, as we will see.

The excess capacity theorem assumes a classical production function and corresponding cost curves as well as the same costs for all producers. Figure 6.4 illustrates the situation. The demand curve is again downward sloping and the slope of marginal revenue curve is twice as much as the demand curve. The marginal cost curve (supply) is upward sloping. As there are some fixed costs, total average costs are U-shaped. Profit maximizing is the quantity $q^{m c}$ where marginal costs equal marginal revenue and the corresponding price is $p^{m c}$. If the average total cost curve lies below the demand curve, the monopolistic competitor generates a profit.

The strength of consumer preferences for a differentiated product is represented in the elasticity of the demand curve. The stronger the preference, the more inelastic will be the demand curve (Figure 6.4, right).

In the short run, the monopolistic competitor will act as monopolist dealing with cost curves from the classical production function (Figure 6.5, left). With market entry, the demand and marginal revenue curves will swivel around point $\mathrm{A}$ and become more elastic. The $y$-intercept moves from B to B’ (Figure 6.5, right). The price is lowered and the offered quantity is also reduced. This reduces the monopolistic profit.

经济代写|微观经济学代写Microeconomics代考|Monopsony

Monopsonies play a role in the construction sector. The government or government agencies act sometimes as the sole buyer in a market. In many countries, it is the exclusive right and duty of the government to provide public roads. As these are by far the majority of all roads, the government acts as monopsonist. The same often holds true for railroads. Thus, monopsonies are of interest. The owner in construction will not be a consumer (one-family home) but an investor and will thus act on factor markets (Chapter 7).

A typical case in the microeconomic literature to explain monopsonies is one employer looking for labor (Nicholson and Snyder 2014). This could be a large firm in a small town. If one producer is the asking for the by-far-largest supply of labor from a relatively large number of workers, then that producer holds a monopsony position. This is the inverse of a monopoly.

If we call $p \cdot \partial q / \partial L$ the marginal value product of labor $\left(M V P_L\right)$, then we know that this must equal the wage if the producer is maximizing the profit in perfectly competitive markets. If we assume diminishing marginal labor productivity, then the $\mathrm{MVP}_{\mathrm{L}}$ curve is downward sloping (Figure 6.8).

The labor supply curve is sloping upward because the monopsonist is not facing a negligible quantity of labor but the majority of the labor supply in a regional market. If the monpsonist hires one more worker, this worker is only willing to accept above market price. If all workers receive the same wage, this means that adding one more worker increases total cost by the pay for the worker and the increase for all other workers. The cost of hiring one more worker is always higher than the market price. Consequently, the marginal expense curve will always be above the labor supply curve.

A producer in a perfectly competitive market will hire more labor until the additional marginal costs $M E_{\mathrm{L}}$ are equal to the additional marginal revenue $M R_{\mathrm{L}}$. If the costs were higher, then the producer would lose money; if the costs were lower, it would forgo the opportunity to increase its profit:
$$
M E_{\mathrm{L}}=M R_{\mathrm{L}}
$$
The monopsonist will add labor until the marginal revenue of labor equals the MVP:
$$
M R_{\mathrm{L}}=M V P_{\mathrm{L}}
$$
If the producer were a price taker, then the intersection of the downward-sloping demand curve and the upward-sloping supply curve would provide the market equilibrium. This is marked as $L_{\mathrm{C}}$ and $w_{\mathrm{C}}$ in Figure 6.9. Since a monopsonist is not a price taker, the marginal revenue curve (expense curve) lies above the supply curve and this determines actual labor demand by $M R_{\mathrm{L}}=M V P_{\mathrm{L}}$. Thus, the monopsonist demands less labor $\left(L_{\mathrm{M}}\right)$ at a lower wage $\left(w_M\right)$ by using its market power.

The more inelastic the labor supply curve is, the lower will the wage be. To see this effect, you just have to rotate the supply curve more upward around the point $L_{\mathrm{C}} / w_{\mathrm{C}}$.

微观经济学代考

经济代写|微观经济学代写Microeconomics代考|Monopolistic Competition

垄断竞争是除异质寡头垄断之外最普遍的市场配置。在这些条件下，生产商提供差异化产品——而不是同质产品——服务于相同的目的，例如 T 恤，消费者对某些产品有偏好。这为生产商设定价格提供了一些空间。他们不再是价格接受者，但他们也没有正常垄断者的自由。他们的市场力量更加有限。生产商可以主要通过风格、位置或质量来区分产品。生产者越能够区分产品，市场力量就越强。每个生产者只向市场提供相对少量的商品，因此其行为不会影响其他生产者。因此，如果生产者提高产品价格，

然而，生产者受到可以进入市场并攻击差异化产品的新公司的威胁。从长远来看，自由市场进入的可能性会使利润减少到零。这个结果与完全竞争相同，但其他结果不同，我们将看到。

产能过剩定理假设一个经典的生产函数和相应的成本曲线以及所有生产者的相同成本。图 6.4 说明了这种情况。需求曲线再次向下倾斜，边际收益曲线的斜率是需求曲线的两倍。边际成本曲线（供给）向上倾斜。由于有一些固定成本，总平均成本呈 U 形。利润最大化是数量q米C其中边际成本等于边际收益，相应的价格是p米C. 如果平均总成本曲线位于需求曲线下方，则垄断竞争者产生利润。

消费者对差异化产品的偏好强度体现在需求曲线的弹性上。偏好越强，需求曲线就越缺乏弹性（图 6.4，右）。

在短期内，垄断竞争者将作为垄断者处理经典生产函数的成本曲线（图 6.5，左）。随着市场进入，需求和边际收益曲线将围绕点旋转A并变得更有弹性。这和-拦截从 B 移动到 B’（图 6.5，右）。价格降低，报价数量也减少。这减少了垄断利润。

经济代写|微观经济学代写Microeconomics代考|Monopsony

垄断在建筑行业发挥作用。政府或政府机构有时充当市场上的唯一买家。在许多国家，提供公共道路是政府的专有权利和义务。由于这些是迄今为止所有道路中的大多数，因此政府充当垄断者。铁路也是如此。因此，芢断是令人感兴趣的。建筑业主将不是消费者（单户住宅），而是投资者，因此将在要素市场上行动（第 7 章)。
微观经济学文献中解释垄断的典型案例是一个雇主在寻找劳动力 (Nicholson 和 Snyder 2014)。这可能是一个小镇上的大公司。如果一个生产者要求相对大量的工人提供迄今为止最大的劳动力供应，那么该生产者就处于垄断地位。这与䞣断相反。
如果我们打电话 $p \cdot \partial q / \partial L$ 劳动的边际价值产品 $\left(M V P_L\right)$ ，那么我们就知道，如果生产者在完全竞争市场上实现利润最大化，那么这一定等于工资。如果我们假设边际劳动生产率递减，那么 $M_V \mathrm{PP}{\mathrm{L}}$ 曲线向下倾斜 (图 6.8)。劳动力供给曲线向上倾斜，因为龿断者面对的不是微不足道的劳动力，而是区域市场中的大部分劳动力供给。如果 monpsonist 再雇用一名工人，这名工人只愿意接受高于市场价格的价格。如果所有工人获得相司的工资，这意味着增加一名工人会增加总成本，增加的部分是该工人的工资和所有其他工人的增加。多蒮一名工人的成本总是高于市场价格。因此，边际费用曲线将始终高于劳动力供给曲线。完全竞争市场中的生产者将雇佣更多的劳动力，直到额外的边际成本 $M E{\mathrm{L}}$ 等于额外的边际收益 $M R_{\mathrm{L}}$. 如果成本更高，那么生产商就会赔钱；如果成本较低，它将放弃增加利润的机会：
$$
M E_{\mathrm{L}}=M R_{\mathrm{L}}
$$
垄断者将增加劳动力，直到劳动力的边际收益等于 MVP：
$$
M R_{\mathrm{L}}=M V P_{\mathrm{L}}
$$
如果生产者是价格接受者，那么向下倾斜的需求曲线和向上倾斜的供给曲线的交点将提供市场均衡。这被标记为 $L_{\mathrm{C}}$ 和 $w_{\mathrm{C}}$ 在图 6.9 中。由于垄断者不是价格接受者，边际收益曲线 (费用曲线) 位于供给曲线之上，这决定了实际劳动力需求 $M R_{\mathrm{L}}=M V P_{\mathrm{L}}$. 因此，垄断者需要更少的劳动力 $\left(L_{\mathrm{M}}\right)$ 以较低的工资 $\left(w_M\right)$ 通过利用其市场力量。
劳动力供给曲线越缺乏弹性，工资就越低。要看到这种效果，您只需将供应曲线围绕该点向上旋转
$$
L_{\mathrm{C}} / w_{\mathrm{C}}
$$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

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