Phy5646/Non-degenerate Perturbation Theory - Problem 3: Difference between revisions
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'''Problem:''' | '''Problem:''' | ||
A charged particle in a simple harmonic oscillator, for which <math>{H}_0 = \frac{p^{2}}{2m} + \frac{mw^{2}}{2}</math>, subject to a constant electric field | A charged particle in a simple harmonic oscillator, for which <math>{H}_0 = \frac{p^{2}}{2m} + \frac{mw^{2}}{2}</math>, | ||
so that <math>{H}^' = q\mathcal{E} x</math>. Calculate the energy shift for the <math>n^{th}</math> level to first and second order in <math>(q\mathcal{E})</math>. | subject to a constant electric field so that <math>{H}^' = q\mathcal{E} x</math>. Calculate the energy shift | ||
for the <math>n^{th}</math> level to first and second order in <math>(q\mathcal{E})</math>. | |||
(Hint: Use the operators <math>a</math> and <math>a^{\dagger}</math> for the evaluation of the matrix elements). | (Hint: Use the operators <math>a</math> and <math>a^{\dagger}</math> for the evaluation of the matrix elements). | ||
Revision as of 03:25, 3 April 2010
(Submitted by Team 1)
This example taken from "Quantum Physics" 3rd ed., Stephen Gasiorowicz, p. 177.
Problem: A charged particle in a simple harmonic oscillator, for which , subject to a constant electric field so that . Calculate the energy shift for the level to first and second order in . (Hint: Use the operators and for the evaluation of the matrix elements).
