Question

A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. What is the average total energy of the oscillator?

Answer 1

The total mechanical energy of a harmonic oscillator is the sum of the potential and kinetic energies of the spring and is given the expression, 

potential energy + kinetic energy 
1/2Kx²+1/2mv²

Answer 2

3KT

Explanation:

As we know that from "equipartition of energy", energy associated with each degree of freedom is $\frac{1}{2} KT$.

The quantum harmonic oscillator has total 6 D.O.F. (3 momentum space & 3coordinate space) hence

<E> = $\frac{6}{2} KT = 3 KT$.