Transcription of Introduction to Perturbation Theory
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Introduction to Perturbation Theory
Physics 342 Lecture 31 Introduction to Perturbation TheoryLecture 31 Physics 342 Quantum Mechanics IMonday, April 21st, 2008 The program of time-independent quantum mechanics is straightforward given a potentialV(x) (in one dimension, say), solve ~22m +V(x) =E ,( )for the eigenstates. These form a complete, orthogonal basis for all this adapted basis, generate generic initial configurations and timeevolve them according to (x,t) = j=1 j j(x)e iEj~t j= (x,0) j.( )At any given time, we have the probability density for the system, and cancalculate various physically measurable properties. If we actually performa measurement, the wavefunction takes on one of the eigenstates (of theoperator associated with the measurement), and returns the value of thephysical measurement for that state (part of our assumption).
31.1. PERTURBATION { POLYNOMIALS Lecture 31 We can see how the = 0 equation (31.5) plays a role here, it is the 0 equation that starts o the process by allowing us to solve for x 0. Notice the cascade here, knowing x 0 = i p c a, we can solve for x 1 (we don’t actually need x 0 to nd x 1 in the current case, but in general, we have a
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