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Consider the following Hamiltonian:
p 1
2+ar
H
2m 2
where y and a are both positive.
(a) Determine the ground state value (i.e. minimum energy) of (r) at T 0.
(b) Determine the frequency for simple harmonic motion for the limit of small temperatures.
(c) Derive an equation for (r) to first order in temperature.

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