A one-dimensional harmonic oscillator has an infinite series of equally spaced energy states, with E x =
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A one-dimensional harmonic oscillator has an infinite series of equally spaced energy states, with Ex = shω, where s is a positive integer or zero, and ω is the classical frequency of the oscillator. We have chosen the zero of energy at the state s = 0
(a) Show that for a harmonic oscillator the free energy is
F = τ log[1 – exp(–hω/τ)] (87)
Note that at high temperatures such that τ >> hω we may expand the argument of the logarithm to obtain F ≈ τ log(hω/τ)
(b) From (87) show that the entropy is
The entropy is shown in figure(a) and the heat capacity in figure(b).
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