A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 201

and we have

where is the probability density. Therefore,

For the quantum mechanical case, there is an equidistant energy

spectrum: (see Problem 4.81) and

To calculate we can use the following trick (assumingJ integer):

From (S.4.82.6) we have

With the familiar sum

we arrive at