Calculate number of microstates of n harmonic oscillators

  1. 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[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.

    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. jcsd
  3. Dick

    Dick 25,893
    Science Advisor
    Homework Helper

    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.
     
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