The energy levels of the harmonic oscillator (neglecting zero point energy) are $\epsilon(n)=$ nhv and $n=0,1,2, \ldots$. Assuming T partition function is :
(a)e
(b)1/e
(c)$1-\frac{1}{e}$
(d)$\frac{1}{1-\frac{1}{e}}$
Answer
Answer (as printed): D
Explanation
We know that $\epsilon(n)=nh\nu$ ......(1) and, assuming $h\nu=k_{B}T$ ......(2).From (1) and (2), the partition function $q=\displaystyle\sum_{n} e^{-nh\nu/k_{B}T}=\dfrac{1}{1-e^{-1}}=\dfrac{1}{1-\frac{1}{e}}$.