Statistics-lab™可以为您提供ust.hk 物理代写|PHYS5310 Statistical Mechanics统计力学课程的代写代考和辅导服务！
PHYS5310 Statistical Mechanics课程简介
Classical mechanics studies the motion of material bodies. It is among the fundamental branches of modern physics and is therefore an essential component of all graduate programs in Physics. This course introduces the structure of classical mechanics and discusses some of its most important applications in modern physics.
In the first part of this course, we will start from the Lagrangian formulation of classical mechanics and study the solution of the equations of motion of several systems, from simple one-body systems, to more complex systems acted upon by central forces and rigid bodies, up to scattering problems and oscillations. We will also extend our discussion to include the theory of special relativity.
The second part of this course will introduce the hamiltonian formulation of classical mechanics and study its formal and physical consequences. More advanced topics, such as non-linear dynamics and continuous systems, will be discussed in the third part of this course, depending on time availability.
PREREQUISITES
Classical mechanics studies the motion of material bodies. It is among the fundamental branches of modern physics and is therefore an essential component of all graduate programs in Physics. This course introduces the structure of classical mechanics and discusses some of its most important applications in modern physics.
In the first part of this course, we will start from the Lagrangian formulation of classical mechanics and study the solution of the equations of motion of several systems, from simple one-body systems, to more complex systems acted upon by central forces and rigid bodies, up to scattering problems and oscillations. We will also extend our discussion to include the theory of special relativity.
The second part of this course will introduce the hamiltonian formulation of classical mechanics and study its formal and physical consequences. More advanced topics, such as non-linear dynamics and continuous systems, will be discussed in the third part of this course, depending on time availability.
PHYS5310 Statistical Mechanics HELP（EXAM HELP， ONLINE TUTOR）
We said in Section 6.1 that perturbation theory can’t be used if the inter-particle potential $v(r)$ diverges as $r \rightarrow 0$. Why not use the Boltzmann factor $\mathrm{e}^{-\beta v(r)}$ as a small parameter for $r \rightarrow 0$ ? What’s wrong with that idea for applying perturbation theory to interacting gases?
Show that the chemical potential of a classical gas can be written in the form
$$
\mu=k T\left[\ln \left(n \lambda_T^3\right)+\ln \left(1-2 b_2 n+\cdots\right)\right] \stackrel{\left|b_2 n\right| \ll 1}{\approx} k T\left[\ln \left(n \lambda_T^3\right)-2 b_2 n+O\left(n^2\right)\right]
$$
Hint: Eq. (6.28). The chemical potential is modified relative to the ideal gas, either positively or negatively, depending on the sign of $b_2$.
Derive Eq. (6.53). Hint: Start with $P=-(\partial F / \partial V)_{T, N}$ (see Table 1.2) and show that (with $n=N / V)$
$$
P=n^2\left(\frac{\partial(F / N)}{\partial n}\right)_T
$$
Then use the relation $-\beta F=\ln Z$, Eq. (4.57). Without fanfare, we’ve been working with the canonical ensemble in Section 6.3.
Suppose there were no near-neighbor interactions in the Ising model $(K=0)$, but we keep the coupling to the magnetic field. Show that in this case $\langle\sigma\rangle$ reduces to one of the Brillouin functions studied in Section 5.2. Which one is it, and does that make sense?
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
Statistics-lab™可以为您提供ust.hk 物理代写|PHYS5310 Statistical Mechanics理论力学课程的代写代考和辅导服务！ 请认准Statistics-lab™. Statistics-lab™为您的留学生涯保驾护航。