Consider the following Hamiltonian: 1 + az 2m 2 where and are both positive

Applications and Investigations in Earth Science (9th Edition)
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ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
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Chapter1: The Study Of Minerals
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Consider the following Hamiltonian:
H =
2m
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.
Transcribed Image Text:Consider the following Hamiltonian: H = 2m 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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