Statistical Mechanics · Problem 2.5

The Canonical Ensemble — R. K. Pathria

Physics — Statistical Mechanics · wkb-quantization-potential-well

Problem

Consider a particle of energy

E

moving in a one-dimensional potential well

V(q)

, such that

m\hbar\left|\frac{dV}{dq}\right| \ll \{m(E-V)\}^{3/2}.

Show that the allowed values of the momentum

p

of the particle are such that

\oint p\, dq = \left(n + \tfrac{1}{2}\right)h,

where

n

is an integer.