# Stat phys problem

#### Pacopag

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 $$\mu$$-canoncal esemble

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

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

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