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## Homework Statement

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[itex]\hbar[/itex]ω + M[itex]\hbar[/itex]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.

## Homework Equations

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

## 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?