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Homework #7
— PHYS 603 — Spring 2007
Deadline:
Tuesday, May 8, 2007, in class
Professor Victor Yakovenko
Oﬃce: 2115 Physics
Web page: http://www2.physics.umd.edu/˜yakovenk/teaching/
Textbook: Gregory H. Wannier,
Statistical Physics
Dover 1987 reprint of the 1966 edition, ISBN 048665401X
Do not forget to write your name and the homework number!
Each problem is worth 10 points.
Ch. 9 Quantum Statistics of Independent Particles
1. Problem 9.1, Applying the three statistics to a twolevel system.
Derive answers analytically. Do not substitute numbers.
2. Problem 9.2, No BoseEinstein condensation for free particle in
D
= 1
,
2
.
3. Problem 9.3, Adiabatic relation holds for any statistics.
You may use virial theorem (2.39).
4. Problem 9.4, Entropy for Fermi statistics.
5. Problem 9.5, Entropy for any statistics.
6. Problem 9.6, Entropy for Bose statistics.
Also read Problem 9.7 and its solution for your information. You don’t need to submit
it, because solution is written in the book.
7. UMD qualiﬁer problem, January 2005: 1D Fermi gas.
Use results of Sec. 144 for this Problem.
Consider a onedimensional (1D) noninteracting free electron gas moving along the
x
axis with a number density of
n
electrons per unit length. Assume the electronic
wavefunctions to be the usual plane wave momentum eigenstates with the electron
energy being quadratic in momentum:
ε
=
p
2
/
2
m
. Give the answers to the questions
below in terms of Planck’s constant ¯
h
, the electron mass
m
, Boltzmann’s constant
k
B
,
the 1D electron density
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 Spring '08
 V.Yakovenco
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