385lec29

# 385lec29 - PHYS 385 Lecture 29 Perturbation theory Lecture...

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PHYS 385 Lecture 29 - Perturbation theory 29 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 29 - Perturbation theory What's important : time-independent perturbation theory Text : Gasiorowicz, Chap. 16 Most of the Hamiltonians that we are faced with in atomic and molecular physics cannot be solved exactly. However, the terms in the Hamiltonian can frequently be arranged in a numerical hierarchy, with some terms having larger numerical values than others. We saw this in the helium atom, where the effect of repulsion between electrons is weaker than the attraction between an electron and a nucleus. There, we solved the problem by discarding the electron repulsion term in favour of an effective charge on the nucleus. In this lecture, we'll do a little better, but still using the idea that we can determine a set of wavefunctions for the most important interaction in the Hamiltonian, then perturb those states by introducing a weaker interaction. We will do this only for time-independent perturbations, and non-degenerate states. Non-degenerate bound states Let's start off with an "unperturbed" Hamiltonian H o whose eigenvalues can be solved analytically. To make the equations less opaque, the Dirac notation is used, where a wavefunction is represented by | E >, and the Schrödinger equation is written H o | E i o > = E i o | E i o >. (1) To this Hamiltonian is added a perturbing interaction V where is a dimensionless parameter, assumed to be small. The complete Hamiltonian obeys H | E

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## This note was uploaded on 09/07/2009 for the course PHYS 385 taught by Professor Davidboal during the Spring '09 term at Simon Fraser.

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385lec29 - PHYS 385 Lecture 29 Perturbation theory Lecture...

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