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>, subject to a constant electric field | ||
so that H | so that <math>{H}^' = q\Epsilon x</math>. Calculate the energy shift for the nth level to first and | ||
second order in (q%). (Hint: Use the operators A and A+ for the evaluation of the matrix elements.) | second order in (q%). (Hint: Use the operators A and A+ for the evaluation of the matrix elements.) | ||
Revision as of 03:09, 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 nth level to first and second order in (q%). (Hint: Use the operators A and A+ for the evaluation of the matrix elements.)
