qual_19_p4_sol.pdf - QUALIFYING EXAMINATION Part 4...

QUALIFYING EXAMINATION, Part 4
Solutions
Problem 1: Statistical Mechanics I
(a) The one-body distribution for a classical ideal gas with a single-particle Hamiltonian
h =
p 2
2 m
+ V
trap
( r ) is f ( r , p ) = N exp[ - β
p 2
2 m
- βV
trap
( r )], where N is a normalization factor.