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(1) When the energy of the system (simple harmonic oscillator) is given by E = (n +;) hw in a heat bath of temperature T, (a) Derive the partition function Z. (b) For high temperature kT » hw, derive the approximate form of Z. (c) Calculate F (Helmholtz free energy), U (internal energy), and S (entropy) of the system.

(1) When the energy of the system (simple harmonic oscillator) is given by E = (n +;) hw in a heat bath of temperature T, (a) Derive the partition function Z. (b) For high temperature kT » hw, derive the approximate form of Z. (c) Calculate F (Helmholtz free energy), U (internal energy), and S (entropy) of the system.

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(1) When the energy of the system (simple harmonic oscillator) is given by E = (n+) ħw in a heat bath of temperature T, (a) Derive the partition function Z. (b) For high temperature kT » ħw, derive the approximate form of Z. (c) Calculate F (Helmholtz free energy), U (internal energy), and S (entropy) of the system.
Transcribed Image Text:(1) When the energy of the system (simple harmonic oscillator) is given by E = (n+) ħw in a heat bath of temperature T, (a) Derive the partition function Z. (b) For high temperature kT » ħw, derive the approximate form of Z. (c) Calculate F (Helmholtz free energy), U (internal energy), and S (entropy) of the system.
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