# Physics GRE Question

• Testing
I'm studying for the Physics GRE and I came across this question. The correct answer is D, but I'm not sure quite how to do it. Any help would be greatly appreciated!

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

(A) (1/2)kT
(B) kT
(C) (3/2)kT
(D) 3kT
(E) 6kT

G01
Homework Helper
Gold Member
You need to show work in order to get help here. What have you tried so far? What concepts, etc. apply? What are your thoughts?

Last edited:
I'm really not sure where to start. I guess I'll just post this in a different part of the forum then.

I'm studying for the Physics GRE and I came across this question. The correct answer is D, but I'm not sure quite how to do it. Any help would be greatly appreciated!

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

(A) (1/2)kT
(B) kT
(C) (3/2)kT
(D) 3kT
(E) 6kT

nicksauce
Homework Helper
Well the equipartition theorem says that each Degree Of Freedom = 1/2KT. Can you think of why there would be 6 DOF?

That's exactly what I was thinking. It seems like the problem basically states that there are 3 degrees of freedom, which would yield an answer of (3/2)kT. However, the answer guide clearly says that the answer is 6kT (this is from an official GRE practice test).

I can't think of why there would be 6 degrees of freedom...

nicksauce
Homework Helper
Ok let's go back to the 1 dimensional harmonic oscillator... How would you write its total energy? How many DOF is that?

Total energy for a 1-dimensional harmonic oscillator is (1/2)kx^2, right? And wouldn't that just be one degree of freedom?

nicksauce
Homework Helper
Total energy of a 1D SHO is (1/2)kx^2 + (1/2)mv^2...

I'm studying for the Physics GRE and I came across this question. The correct answer is D, but I'm not sure quite how to do it. Any help would be greatly appreciated!

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

(A) (1/2)kT
(B) kT
(C) (3/2)kT
(D) 3kT
(E) 6kT

Acording to the Equipartition Theorem, there is a $kt/2$ contribution to the energy from each degree of quadratic freedom in the Hamiltonian. In equation form, the average total energy is $<E> = skT$, where s is the degrees of freedom.

What is the expression for the Hamiltonian for any n-dimensional 1-particle system?