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Stat phys problem

  1. Apr 10, 2008 #1
    1. The problem statement, all variables and given/known data
    I need to find ntropy S(E) for N independent HO's for both the classical and quantum cases,
    using the [tex]\mu[/tex]-canoncal esemble

    2. Relevant equations
    For one classical HO
    [tex]H={p^2 \over{2m}}+{m\omega^2 q^2 \over 2}[/tex]
    For one quantum HO
    [tex]H=\hbar \omega (n+{1\over 2})[/tex]


    3. The attempt at a solution
    I tried to find the partitn function for one HO.
    [tex]W_1={1\over h^3}\int d^3q d^3p \delta(H-E)[/tex]
    [tex]W_1={1\over h^3} [/tex] times volume of 6-sphere with radius E
    [tex]W_1={1\over h^3} {{\pi^3 E^6}\over 6}[/tex]
    So for N HOs
    [tex]W={W_1^N \over {N!}}={1\over h^{3N}} {{\pi^{3N} E^{6N}}\over 6^N}[/tex]
    Then I can use
    [tex]S(E)=k ln(W)[/tex]
    Can anyone verify if I'm on the right track??
     
  2. jcsd
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