## GR0877 Problem 100

**PROBLEM STATEMENT**: The partition function in statistical mechanics can be written as

,

where the index ranges over all possible microstates of a system and is the energy of microstate . For a single quantum mechanical harmonic oscillator with energies

, where

the partition function is given by which of the following?

(A)

(B)

(C)

(D)

(E)

**SOLUTION**: (**E**) The partition function for a single QM harmonic oscillator is:

.

which is an infinite geometric series:

. Thus, .

*Found a typo? Comment!*

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