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Consider a one-dimensional quantum harmonic oscillator, of angular frequency w, at thermal equilibrium at temperature T. a) Find an expression for the entropy of the oscillator. b) Find expressions which give the approximate temperature dependence of the entropy for both low (kBT hw) and high (kBT >> hw) temperatures. c) Consider a system of N such oscillators with frequencies w distributed with equal probability over the range 0and high temperatures.

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