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Unformatted text preview: Lecture 23 November 4, 2009 RayleighSchrdinger perturbation theory Perturbation Theory Exact eigenfunctions, eigenvalues of a simplified operator: possible to estimate eigenfunctions, eigenvalues of a more complete operator. RayleighSchrdinger perturbation theory Some operator A that we can write as (231) A (0) is an operator for which we can find eigenfunctions V is a perturbing operator and is a dimensionless parameter that, as it varies from 0 to 1, maps A (0) into A . A = A (0) + " V Taylor Series Expansion (232) and (233) is the eigenvalue for , appropriate normalized groundstate eigenfunction for A (0) . Ease of notation, eqs. 232 and 233 (234) and (235) superscripts ( n ) n thorder corrections to the zeroth order term, defined by comparison to eqs. 232 and 233. " = " (0) + # $" (0) $# # = + 1 2! # 2 $ 2 " (0) $# 2 # = + 1 3! # 3 $ 3 " (0) $# 3 # = + L a = a (0) + " # a (0) #" " = + 1 2!...
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 Fall '08
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