Consider the following Hamiltonian: p 1 H ² + az* 2m 2 where y and a are both positive. (a) Determine the ground state value (i.e. minimum energy) of (z) 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.
Consider the following Hamiltonian: p 1 H ² + az* 2m 2 where y and a are both positive. (a) Determine the ground state value (i.e. minimum energy) of (z) 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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Transcribed Image Text: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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