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