# hwk5 - (c) Using the result of part (a), calculate the...

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PH421 - Thermal and Statistical Physics Assignment 5 - Jan 30, 2008 1. Quantum partition function of a simple harmonic oscillator . A simple harmonic oscillator (SHO) has its energy eigenvalues given by ± r = ( r + 1 2 ) ~ ω (1) where r = 0 , 1 , 2 , ... (a) Derive the partion function of a SHO in thermal equilibrium at temperature T . (b) Find what is the probability that the SHO is in the ground state when ~ ω >> kT (limit of low temperature)
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Unformatted text preview: (c) Using the result of part (a), calculate the entropy of the SHO in thermal equilibrium at temperature T . Show that, in the limit of T that tends to 0, the entropy tends to S → 0. Explain this results in terms of the result from part (b). 2. Problem 2.3 from textbook 3. Problem 2.5 from textbook 4. Problem 2.6 from textbook 5. Problem 2.7 from textbook...
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## This note was uploaded on 07/22/2011 for the course PH 421 taught by Professor Bonamente during the Spring '09 term at University of Alabama - Huntsville.

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