# Calculate number of microstates of n harmonic oscillators

 P: 15 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?
 Quote by 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?