Entropy of noninteracting distinguishable oscillators
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A detailed solution regarding the entropy of noninteracting distinguishable oscillators is given.
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The energy levels of a harmonic oscillator are given by:
E_n = (n + 1/2) hbar omega (1)
If we have N noninteracting distinguishable oscillators then the energy levels will be given by adding up the energy levels of the individual oscillators. If the k-th oscillator is in quantum state n_k, then:
E_{n1, n2,n3,...,n_N} = hbar omega[(n_1 + 1/2) + (n_2 + 1/2) + (n_3 + 1/2) + ...+ (n_N + 1/2)] =
hbar omega [n_1 + n_2 + n_3 + ...+n_N + N/2]
The average energy per oscillator is thus:
1/N E_{n1, n2,n3,...,n_N} = hbar omega [(n_1 + n_2 + n_3 + ...+ n_N)/N + 1/2]
If the average energy per oscillator is hbar ...
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