## 物理代写|电磁学代写electromagnetism代考|PHYC20014

statistics-lab™ 为您的留学生涯保驾护航 在代写电磁学electromagnetism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磁学electromagnetism代写方面经验极为丰富，各种代写电磁学electromagnetism相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|电磁学代写electromagnetism代考|Electric Field Lines

By definition, electric field lines are drawn to follow the same direction as the electric field vector at any point. Furthermore, the electric field vector is tangent to the line at every point along the field line.

The electric field lines are such that $\mathbf{E}$ is tangent to the electric field line at each point. The number of lines per unit surface area passing a surface perpendicular to the lines is proportional to the magnitude $|\mathbf{E}|$ in that region. Furthermore, the lines are directed radially away from the positive point charge. Moreover, the lines are directed radially toward the negative point charge.

In Fig. 1.7, we show the electric field lines of a negative and positive point charge. It can be seen that for a negative point charge, $-q$, the electric field lines are drawn toward the charge (see Fig. 1.7a). On the other hand, for a positive point charge, $+q$, electric field lines are leaving the charge, as shown in Fig. 1.7b.

The following general rules for drawing electric field lines apply:
The lines start from a positive charge and end on a negative charge. Also, the number of lines drawn, leaving a positive charge, or approaching a negative charge is proportional to the magnitude of the charge. Moreover, no two field lines can cross.

In Fig. 1.8, we show the electric field vector for a positive point charge $+q$ located at the point $(0,3,0)$ (Fig. 1.8b) and a negative point charge $-q$ located at $(0,-3,0)$ (Fig. 1.8a), colored according to the magnitude of the electric field $\mathbf{E}$ using a color scaling. as depicted in Fig. 1.8. Besides, the electric field lines of the resultant electric field are shown in Fig. 1.8c.

## 物理代写|电磁学代写electromagnetism代考|Motion in Uniform Electric Field

Suppose a charge particle of mass $m$ and charge $q$ is moving in a uniform electric field $\mathbf{E}$. Electric field $\mathbf{E}$ exerts on a particle placed in it the force
$$\mathbf{F}=q \mathbf{E}$$

If that force is equal to the resultant force exerted on the particle, it causes the particle to accelerate, based on Newton’s second law:
$$m \mathbf{a}=q \mathbf{E}$$
The acceleration gained by the charge is given as
$$\mathbf{a}=\frac{q}{m} \mathbf{E}$$
Therefore, if $\mathbf{E}$ is uniform (that is, constant in magnitude and direction), then a is constant. Furthermore, if the particle has a positive charge, then its acceleration is in the direction of the electric field. On the other hand, if the particle has a negative charge, then its acceleration is in the direction opposite the electric field.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Motion in Uniform Electric Field

$$\mathbf{F}=q \mathbf{E}$$

$$m \mathbf{a}=q \mathbf{E}$$

$$\mathbf{a}=\frac{q}{m} \mathbf{E}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|电磁学代写electromagnetism代考|ELEC3104

statistics-lab™ 为您的留学生涯保驾护航 在代写电磁学electromagnetism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磁学electromagnetism代写方面经验极为丰富，各种代写电磁学electromagnetism相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|电磁学代写electromagnetism代考|Force Fields

The field forces act through space, producing an effect even when no physical contact between the objects occurs. As an example, we can mention the gravitational field. Michael Faraday developed a similar approach to electric forces. That is, an electric field exists in the region of space around any charged body, and when another charged body is inside this region of the electric field, an electric force acts on it.

Definition 1.2 The electric field $\mathbf{E}$ at a point in space is defined as the electric force $\mathbf{F}_e$ acting on a positive test charge $q_0$ placed at that point divided by the magnitude of the test charge:
$$\mathbf{E}=\frac{\mathbf{F}_e}{q_0}$$

The vector $\mathbf{E}$ has the SI units of newtons per coulomb (N/C). Figure $1.3$ illustrates the electric field $\mathbf{E}$ created by a positively charged sphere with total charge $Q$ at the positive test charge $q_0$. Here, we have assumed that the test charge $q_0$ is small enough that it does not disturb the charge distribution of the sphere responsible for the electric field.

Note that $\mathbf{E}$ is the field produced by some charge external to the test charge, and it is not the field produced by the test charge itself. Also, note that the existence of an electric field is a property of its source. For example, every electron comes with its electric field. An electric field exists at a point if a test charge at rest at that point experiences an electric force. The electric field direction is the direction of the force on a positive test charge placed in the field. Once we know the magnitude and direction of the electric field at some point, the electric force exerted on any charged particle (either positive or negative) placed at that point can be calculated. The electric field exists at some point space, including the free space, independent of the existence of another test charge at that point.

To determine the direction of electric field, consider a point charge $q$ located some distance $r$ from a test positive charge $q_0$ located at a point $P$, as shown in Fig. 1.4. Coulomb’s law defines the force exerted by $q$ on $q_0$ as
$$\mathbf{F}_e=k_e \frac{q q_0}{r^2} \hat{\mathbf{r}}$$
where $\hat{\mathbf{r}}$ represents the usual unit vector directed from $q$ toward $q_0$ (see Fig. 1.4). Electric field created by $q$ (positive or negative) is $$\mathbf{E}=\frac{\mathbf{F}_e}{q_0}=k_e \frac{q}{r^2} \hat{\mathbf{r}}$$
From Eq. (1.11), when $q<0$, then $\mathbf{E}$ is pointing opposite to vector $\hat{\mathbf{r}}$, and hence the electric field of a negative charge is pointing toward that charge, see Fig. 1.4a. On the other hand, when $q>0, \mathbf{E}$ and $\hat{\mathbf{r}}$ are parallel, and hence the electric field of a positive charge is pointing away from that charge, as shown in Fig. 1.4b.

## 物理代写|电磁学代写electromagnetism代考|Superposition Principle

According to superposition principle, at any point $P$, the total electric field due to a set of discrete point charges, $q_1, q_2, \ldots, q_N$, positive and negative charges, is equal to the sum of the individual charge electric field vectors (see Fig. 1.5). Mathematically, we can write
$$\mathbf{E}(\mathbf{r})=\sum_{i=1}^N \mathbf{E}i=\sum{i=1}^N k_e \frac{q_i}{\left|\mathbf{r}-\mathbf{r}_i\right|^2} \hat{\mathbf{r}}_i$$
In Eq. (1.12), $\left|\mathbf{r}-\mathbf{r}_i\right|$ is the distance from $q_i$ to the point $P$ (the location of a test charge), where $\mathbf{r}$ is the position vector of the point $P$ with respect to some reference frame, as indicated in Fig. 1.5, and $\mathbf{r}_i$ is the position vector of the charge $i$ in that reference frame. Furthermore, $\hat{\mathbf{r}}_i$ is a unit vector directed from $q_i$ toward $P$.

Note that in Eq. (1.12) the dependence of $\mathbf{E}$ on only position vector of point $P$. r. assumes a static configuration of the charges in space. That is, for some other configuration distribution of charges in space, $\mathbf{E}$ at the same point $P$ may be different. Note that often for convenience, Eq.(1.12) is also written as $$\mathbf{E}(\mathbf{r})=\sum_{i=1}^N k_e \frac{q_i\left(\mathbf{r}-\mathbf{r}_i\right)}{\left|\mathbf{r}-\mathbf{r}_i\right|^3}$$
where
$$\hat{\mathbf{r}}_i=\frac{\mathbf{r}-\mathbf{r}_i}{\left|\mathbf{r}-\mathbf{r}_i\right|}$$
If the distances between charges in a set of charges are much smaller, compare with the distance of the set from a point where the electric field is to be calculated, then charge distribution is continuous.

To calculate the net electric field created by a continuous charge distribution in some volume $V$, we follow these steps. First, we divide the charge distribution into macroscopically small elements with small charge $\Delta q_i$, as shown in Fig. 1.6a. $\Delta q_i=\rho_i \Delta V$, where $\rho_i$ is seen from a microscopic viewpoint as a uniform charge density within the volume element $i$, which represents one of the possible configurations of microscopic description. It is important to note that with “macroscopically small” we should understand a small volume in space with a characteristic microscopic configuration of the charges inside it that can, on average, macroscopically be represented as a point-like charge, $\Delta q_i$. Then, we calculate the electric field due to one of these macroscopically point charges, $\Delta q_i$, at some point $P$ at distance $\left|\mathbf{r}-\mathbf{r}_i\right|$ from the charge element, $\Delta q_i$, as
$$\Delta \mathbf{E}\left(\mathbf{r}, \mathbf{r}_i\right)=k_e \frac{\Delta q_i}{\left|\mathbf{r}-\mathbf{r}_i\right|^2} \hat{\mathbf{r}}_i$$
where $\hat{\mathbf{r}}_i$ is a unit vector directed from the charge element $\Delta q_i$ toward $P$. Here, $\mathbf{r}$ is position vector of point $P$ in some reference frame, and $\mathbf{r}_i$ is the position vector of the macroscopically point charge $\Delta q_i$.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Force Fields

$$\mathbf{E}=\frac{\mathbf{F}_e}{q_0}$$

$$\mathbf{F}_e=k_e \frac{q q_0}{r^2} \hat{\mathbf{r}}$$

$$\mathbf{E}=\frac{\mathbf{F}_e}{q_0}=k_e \frac{q}{r^2} \hat{\mathbf{r}}$$

## 物理代写|电磁学代写electromagnetism代考|Superposition Principle

$$\mathbf{E}(\mathbf{r})=\sum_{i=1}^N \mathbf{E} i=\sum i=1^N k_e \frac{q_i}{\left|\mathbf{r}-\mathbf{r}i\right|^2} \hat{\mathbf{r}}_i$$ 在等式中。(1.12)， $\left|\mathbf{r}-\mathbf{r}_i\right|$ 是距离 $q_i$ 直截了当 $P$ (测试电荷的位置)，其中 $\mathbf{r}$ 是点的位置向量 $P$ 关于一些 参考系，如图 1.5 所示，以及 $\mathbf{r}_i$ 是电荷的位置向量 $i$ 在那个参考系中。此外， $\hat{\mathbf{r}}_i$ 是指向的单位向量 $q_i$ 朝向 $P$. 请注意，在等式中。(1.12) 的依赖 $\mathbf{E}$ 仅在点的位置向量上 $P$. 河 假定空间中电荷的静态配置。也就是说， 对于空间中电荷的一些其他配置分布， $\mathbf{E}$ 在同一时间 $P$ 可能不同。请注意，通常为方便起见，Eq.(1.12) 也写为 $$\mathbf{E}(\mathbf{r})=\sum{i=1}^N k_e \frac{q_i\left(\mathbf{r}-\mathbf{r}_i\right)}{\left|\mathbf{r}-\mathbf{r}_i\right|^3}$$

$$\hat{\mathbf{r}}_i=\frac{\mathbf{r}-\mathbf{r}_i}{\left|\mathbf{r}-\mathbf{r}_i\right|}$$

$$\Delta \mathbf{E}\left(\mathbf{r}, \mathbf{r}_i\right)=k_e \frac{\Delta q_i}{\left|\mathbf{r}-\mathbf{r}_i\right|^2} \hat{\mathbf{r}}_i$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|电磁学代写electromagnetism代考|PHYS3040

statistics-lab™ 为您的留学生涯保驾护航 在代写电磁学electromagnetism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磁学electromagnetism代写方面经验极为丰富，各种代写电磁学electromagnetism相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|电磁学代写electromagnetism代考|Electrical Charges

There exist several simple experiments to demonstrate the existence of electrical charges and forces. For example,

1. When we comb our hair on a dry day, we find that the comb attracts pieces of paper.
2. The same effect of attracting pieces of paper occurs when materials such as glass or rubber are rubbed with silk or fur.

As a general rule, for every material behaving in that way, we can say that it is electrified, or it becomes electrically charged.

Benjamin Franklin (1706-1790) found that there exist two types of electric charges, namely positive and negative. The following experiment can be used to demonstrate his finding. Suppose that we rubber with fur a hard rubber rod. In addition, we rub a glass rod with silk material. Then, if the glass rod is brought near the rubber rod, we will observe that the two attract each other. However, if we bring near each other two charged rubber rods or two charged glass rods, then the two repel each other. This experiment indicates the existence of two different states of electrification for the rubber and glass. Furthermore, it finds that like charges repel each other and unlike charges attract each other.

By convention, the electric charge on the glass rod is positive, and that on the rubber rod is negative. Based on that convention, any charged object repelled by another charged object must have the same sign of charge with it, and any charged object attracted by another charged object must have an opposite sign of charge. It is important to note that the electricity model of Franklin implies that electric charge is always conserved. That is, an electrified state (positive or negative) is due to the charge transfer from one object to the other. In other words, when an object gains some amount of positive/negative charge, then the other gains an equal amount of the electric charge of the opposite sign.

Robert Millikan (1868-1953), in 1909, discovered that electric charge always appears as a multiple integer of a fundamental amount of charge, called $e$ such that the electric charge $q$, which is a standard symbol for the charge, is quantized as
$$q=N e$$
Here, $N$ is an integer number, $N=0, \pm 1, \pm 2, \ldots$.

## 物理代写|电磁学代写electromagnetism代考|Coulomb’s Law

Based on an experiment performed by Coulomb, the electric force between two charged particles at rest is proportional to the inverse of the square of distance $r$ between them and directed along the line joining the two particles. In addition, the electric force is proportional to the charges $q_1$ and $q_2$ on each particle. Also, the electric force is attractive if the charges are of opposite sign and repulsive if the charges have the same sign. That is known as Coulomb’s Law.

Definition 1.1 Force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. Mathematically, the law may be written as
$$F=k_e \frac{\left|q_1\right|\left|q_2\right|}{r^2}$$
In Eq. (1.2), $k_e$ is the Coulomb constant. Note that, in SI, the unit of charge is the coulomb (C). Therefore, the Coulomb constant $k_e$ in SI units has the value
$$k_e=8.9875 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2$$
Often, the constant is written as $$k_e=\frac{1}{4 \pi \epsilon_0}$$
where $\epsilon_0$ is the permittivity of free space given by
$$\epsilon_0=8.8542 \times 10^{-12} \mathrm{C}^2 / \mathrm{N} \cdot \mathrm{m}^2$$
Coulomb’s force is a vector; hence it has a magnitude expressed by Eq. (1.2) and a direction. Therefore, the Coulomb’s law can be expressed in vector form concerning the electric force, $\mathbf{F}{12}$, exerted by the charge $q_1$ (positive or negative) on another charge $q_2$ (positive or negative) as $$\mathbf{F}{12}=k_e \frac{q_1 q_2}{r^2} \hat{\mathbf{r}}$$
In Eq. (1.6), $\hat{\mathbf{r}}$ denotes a unit vector pointing from $q_1$ to $q_2$. Note that based on the Newton’s third law, the electric force, $\mathbf{F}{21}$, exerted by a charge $q_2$ (positive or negative) on a second charge $q_2$ (positive or negative) is $$\mathbf{F}{21}=-\mathbf{F}_{12}$$
Figure $1.1$ illustrates graphically the direction of Coulomb’s force vectors for different combinations of the pairs of positive and negative charges, namely negativenegative, positive-positive, and negative-positive charge-charge interactions.

# 电磁学代考

## 物理代写|电磁学代写electromagnetism代考|Electrical Charges

1. 当我们在干燥的日子㓍头时，我们发现㓍子会吸引纸片。
2. 当玻璃或橡胶等材料与丝绸或毛皮摩擦时，也会产生吸引纸片的相同效果。
作为一般规则，对于以这种方式表现的每种材料，我们可以说它带电，或者带电。
本杰明·富兰克林 (1706-1790) 发现存在两种电荷，即正电荷和负电荷。下面的实验可以用来证明他的 发现。假设我们用毛皮橡胶一根硬橡胶棒。此外，我们用丝绸材料摩擦玻璃棒。然后，如果将玻璃棒靠 近橡胶棒，我们会观察到两者相互吸引。但是，如果我们将两根带电的橡胶棒或两根带电的玻璃棒靠 近，那么两者就会相互排斥。该实验表明橡胶和玻璃存在两种不同的带电状态。此外，它发现同种电荷 相互排斥，不同种电荷相互吸引。
按照惯例，玻璃棒上的电荷为正，橡胶棒上的电荷为负。根据该约定，任何被另一个带电物体排斥的带 电物体必须具有与其相同的电荷符号，而任何被另一个带电物体吸引的带电物体必须具有相反的电荷符 号。重要的是要注意富兰克林的电模型意味着电荷总是守恒的。也就是说，带电状态 (正或负) 是由于 电荷从一个物体转移到另一个物体。换句话说，当一个物体获得一定量的正/负电荷时，另一个物体获得 等量的相反符号的电荷。

Robert Millikan (1868-1953) 在 1909 年发现电荷总是以基本电荷量的整数倍形式出现，称为 $e$ 这样电荷 $q$ ，这是电荷的标准符号，被量化为
$$q=N e$$

## 物理代写|电磁学代写electromagnetism代考|Coulomb’s Law

$$F=k_e \frac{\left|q_1\right|\left|q_2\right|}{r^2}$$

$$k_e=8.9875 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2$$

$$k_e=\frac{1}{4 \pi \epsilon_0}$$

$$\epsilon_0=8.8542 \times 10^{-12} \mathrm{C}^2 / \mathrm{N} \cdot \mathrm{m}^2$$

$$\mathbf{F} 12=k_e \frac{q_1 q_2}{r^2} \hat{\mathbf{r}}$$

$$\mathbf{F} 21=-\mathbf{F}_{12}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|量子力学代写quantum mechanics代考|PHYS3034

statistics-lab™ 为您的留学生涯保驾护航 在代写量子力学quantum mechanics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。我们的专家在代写量子力学quantum mechanics代写方面经验极为丰富，各种代写量子力学quantum mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Quantum Lagrangian

For each $\Psi \in \sec (\boldsymbol{E}, \boldsymbol{Q})$, we obtain the gauge independent and observer independent quantum lagrangian (see Theorem 17.5.2)
$$\left.\mathrm{L}[\Psi]:=-d t \wedge\left(\mathrm{imh}\eta(\Psi, \text { д }\lrcorner \nabla^{\uparrow} \Psi\right)+\frac{1}{2}\left(\bar{G} \otimes \mathrm{h}\eta\right)\left(\check{\nabla}^{\uparrow} \Psi, \check{\nabla}^{\dagger} \Psi\right)\right): \boldsymbol{E} \rightarrow \Lambda^4 T^{\dagger} \boldsymbol{E},$$
with observed and coordinate expressions
\begin{aligned} & \mathrm{L}[\Psi]=-d t \wedge\left(\mathrm{imh}\eta\left(\Psi, \nabla{\nexists[o]}[o] \Psi\right)+\frac{1}{2}\left(\bar{G} \otimes \mathrm{h}_\eta\right)(\nabla[o] \Psi, \nabla[o] \Psi)\right), \ & \mathrm{L}[\Psi]=\frac{1}{2}\left(-G_0^{i j} \partial_i \bar{\psi} \partial_j \psi+\mathfrak{i}\left(\bar{\psi} \partial_0 \psi-\psi \partial_0 \bar{\psi}\right)-\mathfrak{i} A_0^j\left(\bar{\psi} \partial_j \psi-\psi \partial_j \bar{\psi}\right)+2 \alpha_0 \bar{\psi} \psi\right) v^0 ; \ & \end{aligned}

With reference to the distinguished quantum basis $b_{\Psi}$, the distinguished observer $o_{\Psi}$, and the potential $A[\Psi]$ “seen by” $\Psi$, the above expression can be written in the following remarkable way (see Theorem 15.2.31 and Corollary 17.5.3)
$$\mathrm{L}[\Psi]=\left(\frac{1}{2} \bar{G}(d|\Psi|, d|\Psi|)+A[\Psi]|\Psi|^2\right) \otimes v .$$
We stress that, here again, the explicit mention of the phase polar degree of freedom of the quantum particle $((\Psi))$ disappears; however, it is implicitly encoded in $A[\Psi]$.

According to the standard lagrangian formalism, for each $\Psi \in \sec (\boldsymbol{E}, \boldsymbol{Q})$, we obtain the “quantum momentum form” (see Proposition 17.5.7)
$$\mathrm{P}:=\vartheta_Q \bar{\wedge} V_Q \mathrm{~L}: J_1 \boldsymbol{Q} \rightarrow \Lambda^4 T^* \boldsymbol{Q},$$
with coordinate expression
\begin{aligned} \mathrm{P}= & \frac{1}{2} \mathfrak{i}(\bar{z} d z-z d \bar{z}) \wedge v_0^0-\frac{1}{2}\left(G_0^{i j}\left(\bar{z}_i d z+z_i d \bar{z}\right)+\mathfrak{i} A_0^j(z d \bar{z}-\bar{z} d z)\right) \wedge v_j^0 \ & +\left(-\frac{1}{2} \mathfrak{i}\left(\bar{z} z_0-z \bar{z}_0\right)+\frac{1}{2}\left(G_0^{i j}\left(\bar{z}_i z_j+z_i \bar{z}_j\right)+\mathfrak{i} A_0^j\left(z \bar{z}_j-\bar{z} z_j\right)\right)\right) v^0 . \end{aligned}

## 物理代写|量子力学代写quantum mechanics代考|Schrödinger Operator

For each $\Psi \in \sec (\boldsymbol{E}, \boldsymbol{Q})$, we obtain the gauge independent and observer independent Schrödinger operator (see Theorem 17.6.5 and [219])
$$\left.\mathrm{S}[\Psi]:=\frac{1}{2}(\text { д }\lrcorner \nabla^{\uparrow} \Psi+\delta^{\uparrow}(Q[\Psi])\right) \in \sec \left(\boldsymbol{E}, \mathbb{T}^* \otimes \boldsymbol{Q}\right),$$
with observed and coordinate expression

\begin{aligned} & \mathrm{S}[\Psi]=\nabla[o]{\mu[o]} \Psi+\frac{1}{2} \operatorname{div}\eta \mu[o] \Psi-\mathfrak{i} \frac{1}{2} \Delta[G, o] \Psi, \ & \mathrm{S}[\Psi]=\left(\partial_0 \psi-\frac{1}{2} \mathrm{i} G_0^{i j} \partial_{i j} \psi-\left(A_0^j+\frac{1}{2} \mathrm{i} \frac{\partial_i\left(G_0^{i j} \sqrt{|g|}\right)}{\sqrt{|g|}}\right) \partial_j \psi\right. \ & \left.+\frac{1}{2}\left(\frac{\partial_0 \sqrt{|g|}}{\sqrt{|g|}}-\frac{\partial_i\left(A_0^i \sqrt{|g|}\right)}{\sqrt{|g|}}-\mathfrak{i} 2 \alpha_0\right) \psi\right) u^0 \otimes \mathrm{b} . \ & \end{aligned}
Several authors say that the Schrödinger equation is observer dependent; this fact happens if we consider an arbitrary phenomenological potential. But, if we deal with the joined gravitational and electromagnetic potential, then the Schrödinger equation turns out to be observer equivariant. In fact, the above joined potential fulfills a distinguished transition law (determined by the upper quantum connection), which turns out to be responsible for the observer equivariance of the Schrödinger equation. Of course, a possible additional phenomenological potential might be added by hand to our Schrödinger equation, but so doing we would break the covariance of the equation.

With reference to the distinguished quantum basis $\mathrm{b}{\Psi}$, the distinguished observer $o{\Psi}$, and the potential $A[\Psi]$ “seen by” $\Psi$, the above expression can be written in the following remarkable way (see Corollary 17.6.9)
$$\mathrm{S}[\Psi]=\left(\text { д }\left[o_{\Psi}\right] \cdot|\Psi|+\frac{1}{2}|\Psi| \operatorname{div}\eta \text { д }\left[o{\Psi}\right]-\mathfrak{i}\left(\frac{1}{2} \Delta[G]|\Psi|+A[\Psi]\right)|\Psi|\right) \otimes \mathrm{b}_{\Psi} .$$

## 物理代写|量子力学代写quantum mechanics代考|Quantum Lagrangian

$$\left.\mathrm{L}[\Psi]:=-d t \wedge\left(\operatorname{imh} \eta(\Psi, \Omega\lrcorner \nabla^{\uparrow} \Psi\right)+\frac{1}{2}(\bar{G} \otimes \mathrm{h} \eta)\left(\check{\nabla}^{\uparrow} \Psi, \check{\nabla}^{\dagger} \Psi\right)\right): \boldsymbol{E} \rightarrow \Lambda^4 T^{\dagger} \boldsymbol{E},$$

$$\mathrm{L}[\Psi]=-d t \wedge\left(\operatorname{imh} \eta(\Psi, \nabla \nexists[o][o] \Psi)+\frac{1}{2}\left(\bar{G} \otimes \mathrm{h}_\eta\right)(\nabla[o] \Psi, \nabla[o] \Psi)\right), \quad \mathrm{L}[\Psi]=\frac{1}{2}\left(-G_0^{i j}\right.$$

$$\mathrm{L}[\Psi]=\left(\frac{1}{2} \bar{G}(d|\Psi|, d|\Psi|)+A[\Psi]|\Psi|^2\right) \otimes v$$

$$\mathrm{P}:=\vartheta_Q \bar{\wedge} V_Q \mathrm{~L}: J_1 \boldsymbol{Q} \rightarrow \Lambda^4 T^* \boldsymbol{Q},$$

$$\mathrm{P}=\frac{1}{2} \mathrm{i}(\bar{z} d z-z d \bar{z}) \wedge v_0^0-\frac{1}{2}\left(G_0^{i j}\left(\bar{z}_i d z+z_i d \bar{z}\right)+\mathfrak{i} A_0^j(z d \bar{z}-\bar{z} d z)\right) \wedge v_j^0 \quad+\left(-\frac{1}{2} \mathrm{i}\left(\bar{z} z_0\right.\right.$$

## 物理代写|量子力学代写quantum mechanics代考|Schrödinger Operator

$$\left.\mathrm{S}[\Psi]:=\frac{1}{2}(\text { ㅍ. }\lrcorner \nabla^{\uparrow} \Psi+\delta^{\uparrow}(Q[\Psi])\right) \in \sec \left(\boldsymbol{E}, \mathbb{T}^* \otimes \boldsymbol{Q}\right),$$

$$\mathrm{S}[\Psi]=\nabla[o] \mu[o] \Psi+\frac{1}{2} \operatorname{div} \eta \mu[o] \Psi-\mathrm{i} \frac{1}{2} \Delta[G, o] \Psi, \quad \mathrm{S}[\Psi]=\left(\partial_0 \psi-\frac{1}{2} \mathrm{i} G_0^{i j} \partial_{i j} \psi-\left(A_0^j\right.\right.$$

$$\mathrm{S}[\Psi]=\left(\text { д }\left[o_{\Psi}\right] \cdot|\Psi|+\frac{1}{2}|\Psi| \operatorname{div} \eta \text { д }[o \Psi]-\mathrm{i}\left(\frac{1}{2} \Delta[G]|\Psi|+A[\Psi]\right)|\Psi|\right) \otimes \mathrm{b}_{\Psi} .$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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

statistics-lab™ 为您的留学生涯保驾护航 在代写量子力学quantum mechanics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。我们的专家在代写量子力学quantum mechanics代写方面经验极为丰富，各种代写量子力学quantum mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Kinetic Quantum Vector Field

For each proper quantum section $\Psi \in \sec \left(\boldsymbol{E}, \boldsymbol{Q}_{/ 0}\right)$, we obtain the gauge independent and observer independent “kinetic quantum vector field” (see Corollary 17.3.5)
$$\mathrm{Q}[\Psi] / \Psi \in \sec \left(\boldsymbol{E},\left(\mathbb{T}^* \otimes T \boldsymbol{E} \otimes \mathbb{C}\right)\right),$$
with observed and coordinate expression
\begin{aligned} \mathrm{Q}[\Psi] / \Psi & =\left(\text { д }[o]+\vec{\nabla}^\omegao)+\mathrm{i} \vec{d}|\Psi|\right) \ & =\left(\partial_0-\left(\mathrm{i} G_0^{i j} \partial_j \psi / \psi+A_0^i\right) \partial_i\right) \otimes u^0 . \end{aligned}

In particular, with reference to the distinguished “rest observer” $o_{\Psi}$ associated with the proper quantum section $\Psi$, we have the splitting (see Corollary 17.3.5)
$$\mathrm{Q}[\Psi] / \Psi=\mathrm{V}[\Psi]-\mathfrak{i} \vec{d} \log |\Psi|$$
into real and imaginary components, which are related, respectively, to the real polar degrees of freedom of the quantum particle (see sect. 1.5.4 and Proposition 14.7.2).
We stress that an analogous splitting would have no meaning for $Q[\Psi]$.

## 物理代写|量子力学代写quantum mechanics代考|Quantum Probability Current

For each $\Psi \in \sec (\boldsymbol{E}, \boldsymbol{Q})$, we obtain the gauge independent and observer independent quantum probability current (see Theorem 17.4.2)
$$J[\Psi]:=\text { д } \otimes|\Psi|^2-\operatorname{reh}\left(\Psi, i \overrightarrow{\nabla^{\uparrow}} \Psi\right) \in \sec \left(\boldsymbol{E}, \mathbb{L}^{-3} \otimes\left(\mathbb{T}^* \otimes T \boldsymbol{E}\right)\right),$$
with observed and coordinate expressions
\begin{aligned} J[\Psi] & =|\Psi|^2 \text { д[o] – re h }(\Psi, i \vec{\nabla}[o] \Psi) \ & =\left(|\psi|^2 \partial_0+\left(i \frac{1}{2} G_0^{i j}\left(\psi \partial_j \bar{\psi}-\bar{\psi} \partial_j \psi\right)-A_0^i|\psi|^2\right) \partial_i\right) \otimes u^0 . \end{aligned}
In particular, for each proper quantum section $\Psi \in \sec \left(\boldsymbol{E}, Q_{/ 0}\right)$, we have the expression $J[\Psi]=|\Psi|^2 V[\Psi]$, which emphasises the role of the two real polar degrees of freedom of the quantum particle.

In view of the discussion of quantum currents, it is convenient to introduce also the quantum probability form $\left[[\Psi]:=i_{[}[\Psi] v \in \sec \left(\boldsymbol{E}, \Lambda^3 T \boldsymbol{E}\right)\right.$, with coordinate expression $\left[[\Psi]=\left(|\psi|^2 v_0^0+\left(\mathrm{i} \frac{1}{2} G_0^{i j}\left(\psi \partial_j \bar{\psi}-\bar{\psi} \partial_j \psi\right)-A_0^i|\psi|^2\right) v_i^0\right)\right.$ (see Proposition 3.2.4).

## 物理代写|量子力学代写quantum mechanics代考|Kinetic Quantum Vector Field

(见推论 17.3.5)
$$\mathrm{Q}[\Psi] / \Psi \in \sec \left(\boldsymbol{E},\left(\mathbb{T}^* \otimes T \boldsymbol{E} \otimes \mathbb{C}\right)\right),$$

$\$ \、begin { aligned } \mid vec {\mathrm{d}}|\backslash \mathrm{Psi}| \backslash \ight) \backslash \mathrm{u}^{\wedge} 0 。 结束 { 对齐} \ \

$$\mathrm{Q}[\Psi] / \Psi=\mathrm{V}[\Psi]-\mathrm{i} \vec{d} \log |\Psi|$$

## 物理代写|量子力学代写quantum mechanics代考|Quantum Probability Current

$$J[\Psi]:=\text { д } \otimes|\Psi|^2-\operatorname{reh}\left(\Psi, i \overrightarrow{\nabla^{\uparrow}} \Psi\right) \in \sec \left(\boldsymbol{E}, \mathbb{L}^{-3} \otimes\left(\mathbb{T}^* \otimes T \boldsymbol{E}\right)\right),$$

$$J[\Psi]=|\Psi|^2 \text { д }[\mathrm{o}]-\operatorname{reh}(\Psi, i \vec{\nabla}[o] \Psi) \quad=\left(|\psi|^2 \partial_0+\left(i \frac{1}{2} G_0^{i j}\left(\psi \partial_j \bar{\psi}-\bar{\psi} \partial_j \psi\right)-A_0^i|\psi|^2\right)\right.$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。