Name:
PHY 5524: Statistical Mechanics, Spring 2013
February 11th , 2013
Midterm Exam # 1
Always remember to write full work for what you do. This will help your grade in
case of incomplete or wrong answers. Also, no credit will be given for an answer, eve
PHY 5524: Statistical Mechanics
April 10th , 2013
Assignment # 12, Solutions
Problem 1
An ideal Bose gas that is in contact with a thermal/particle reservoir at temperature
T and chemical potential obeys the following non-relativistic dispersion relation,
Name:
PHY 5524: Statistical Mechanics, Spring 2013
April 1st , 2013
Midterm Exam # 2, Solutions
Always remember to write full work for what you do. This will help your grade in
case of incomplete or wrong answers. Also, no credit will be given for an answ
PHY 5524: Statistical Mechanics
April 17th , 2013
Assignment # 13, Solutions
Problem 1
Consider the problem of the vibrational modes in a solid satisfying the following dispersion relation,
(k) = A|k|s Ak s ,
where A and s are positive constants, is the
PHY 5524: Statistical Mechanics
March 6th , 2013
Assignment # 9, Solutions
Problem 1
A degenerate electron gas of N particles is conned to a volume V that is in contact with
a thermal bath at zero temperature and placed in a constant magnetic eld B = B.
z
PHY 5524: Statistical Mechanics
March 27th , 2013
Assignment # 10, Solutions
Problem 1
An ideal Bose gas that is in contact with a thermal/particle reservoir at a temperature
T and chemical potential obeys the following dispersion relation,
(p) = A|p| Ap
PHY 5524: Statistical Mechanics
April 3rd , 2013
Assignment # 11, Solutions
Problem 1
An ideal Bose gas contained in a box of xed volume V consists of N noninteracting
bosons of mass M each of which possesses an internal degree of freedom which can
be des
PHY 5524: Statistical Mechanics
February 27th , 2013
Assignment # 8, Solutions
Problem 1
The thermodynamic potential (often called the Landau or grand potential ) for a Bose/Fermi
system is given by,
Q(, T, V )B/F =
e(Ek )/kB T
ln 1
,
k
where the sum is o
PHY 5524: Statistical Mechanics
February 20th , 2013
Assignment # 7, Solutions
Problem 1
Two non-interacting particles inhabit a potential well such that the orbital motion of
each particle gives rise to an energy spectrum E (n) = n , the nth energy level
PHY 5524: Statistical Mechanics
February 6th , 2013
Assignment # 5, Solutions
Problem 1
Consider a classical system of N non-interacting diatomic molecules enclosed in a box of volume
V at temperature T . The Hamiltonian for a single molecule is,
H (p1 ,
PHY 5524: Statistical Mechanics
January 30th , 2013
Assignment # 4, Solutions
Problem 1
Consider the problem of N spin-1/2 particles (e.g. electrons) occupying the N sites of a onedimensional lattice in the presence of a constant magnetic eld B = B0.
z
1.
PHY 5524: Statistical Mechanics
January 23rd , 2013
Assignment # 3, Solutions
Problem 1
Consider a system of N identical but distinguishable particles, each of which has two energy levels
( ). Using the microcanonical ensemble,
1.a) nd the entropy of the
PHY 5524: Statistical Mechanics
January 16th, 2013
Assignment # 2, Solutions
Problem 1
Consider the problem of an isolated particle of mass m moving freely in a one-dimensional box of
size L. Such a particle satises the following one-dimensional Schrdinge
PHY 5524: Statistical Mechanics
February 13th , 2013
Assignment # 6, Solutions
Problem 1
We have shown in class that in the canonical ensemble, where the energy of the system uctuates,
the mean-square uctuations in the energy is related to the specic heat