# Calculate number of microstates of n harmonic oscillators

1. Jan 21, 2013

### opaka

1. The problem statement, all variables and given/known data
Consider a system of N localized particles moving under the influence of a quantum, 1D, harmonic oscillator potential of frequency ω. The energy of the system is given by
E=(1/2)N$\hbar$ω + M$\hbar$ω

where M is the total number of quanta in the system.

compute the total number of microstates as a function of N and M.

2. Relevant equations

not sure. Maybe the volume of a 1N dimentional sphere?

3. The attempt at a solution
My first attempt was simply (M+N-1)!/(M)!(N-1)!
but I was re reading the text, and was wondering if I should back up and use the procedure outlined for the ideal gas, but using the positive 1/8 of a 1N dimentional sphere rather than a 3N dimentional sphere. Any thoughts?

2. Jan 21, 2013

### Dick

I think your first answer is the correct one. You are just trying to figure out how to put M indistinguishable objects into N distinguishable boxes.