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Problem Set 5 for Statistical Physics Course - Physics 831, Assignments of Statistical mechanics

Michigan State University (MSU)Statistical mechanics

Problem set 5 for the statistical physics course, physics 831. The problems cover various topics such as the gamma function, identical gases, and kinetic energy of non-relativistic atoms. Students are required to use the steepest descent method, find probability densities, averages, and root mean square fluctuations.

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Pre 2010

Uploaded on 07/23/2009

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Physics 831 - 2002
Statistical Physics
Problem Set 5
1. Use the steepest descent method to calculate the Gamma function Γ(z+ 1/2) for large z(5
pt)
2. Problem 6.4 for identical gases (3 pt)
3. For a classical system of interacting non-relativistic atoms of mass mat temperature T,
find the probability density for an atom to have a kinetic energy ε. Find the average kinetic
energy and the root mean square fluctuation of the kinetic energy (6 pt)
4. Problem 7.4 (6 pt)
5. Problem 7.6 [the problem is about atoms, not molecules] (6 pt)
6. Problem 7.5 (6 pt)
The problems are from Kerson Huang, Statistical Mechanics, 2nd edition, (Wiley, NY 1987).

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Physics 831 - 2002

Statistical Physics

Problem Set 5

  1. Use the steepest descent method to calculate the Gamma function Γ(z + 1/2) for large z ( pt)
  2. Problem 6.4 for identical gases (3 pt)
  3. For a classical system of interacting non-relativistic atoms of mass m at temperature T , find the probability density for an atom to have a kinetic energy ε. Find the average kinetic energy and the root mean square fluctuation of the kinetic energy (6 pt)
  4. Problem 7.4 (6 pt)
  5. Problem 7.6 [the problem is about atoms, not molecules] (6 pt)
  6. Problem 7.5 (6 pt)

The problems are from Kerson Huang, Statistical Mechanics, 2nd edition, (Wiley, NY 1987).