Finding degeneracy of N Quantum Harmonic Oscillator

[Sekonda]

Hey guys,

For a particular problem I have to determine the total degeneracy across N 3-D Quantum Harmonic oscillators.

Given that the degree of degeneracy for a 3-D harmonic oscillator is given by:

(n+1)(n+2)/2

and the Total energy of N 3d quantum harmonic oscillators is given by the sum of E(i) from i=1 to 3N, or the sum of ((n(i)+0.5))*(hbar)w.

I think I need to sum the degeneracy equation from n(i) i=1 to 3N to find the total number of degeneracies but I'm not sure what sum this reduces to!

Thanks,
Tom

 

[conquest]

Why exactly are you summing up to 3N when you have N harmonic oscillators? To get the energy of a certain state you should add the energy of all the oscialltors right. Then this is summation until N. For every one of these N things there are (n+1)(n+2)/2 different states that yield the same energy. Now you will need explicitly the energies to see in how many ways you can add N energies to get the same one. Then mulitply that by the degeneracy of 1 to the third power.

That is how I would do it at least.

 

[Sekonda]

Indeed, that is how I thought the problem should be worded. However the problem seems to be set out in an unfamiliar way and I'm not quite sure what is meant by the problem at all!

Though, from what you've said is what I've read around various places of the internet. Oh well, will just have to wait and see what the solution is and try and make sense of it then!

Thanks again conquest,
S