348-problem42 - 1 2 4 ( ) / 2 ( ;0) x x ip x x e α π--+...

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Chem. 540 Instructor: Nancy Makri PROBLEM 42 In class we calculated the time-dependent Green function or propagator for a free particle of mass m moving in one dimension. a) Using the one-dimensional result, find the propagator for a free particle moving in three di - mensions. b) Calculate the time evolution of a wave packet moving in free one-dimensional space given that at 0 t = its wavefunction has the form
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Unformatted text preview: 1 2 4 ( ) / 2 ( ;0) x x ip x x e α π--+ Ψ = h . Check your answer by directly substituting in the time-dependent Schrödinger equation. Examine how the probability density spreads with time by calculating the “uncertainty in position” ( 29 1 2 2 2 ( ) ( ) ( ) ( ) ( ) x t t x t t x t ∆ = Ψ Ψ- Ψ Ψ ....
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This note was uploaded on 02/08/2012 for the course CHEM 540 taught by Professor Mccall during the Fall '08 term at University of Illinois, Urbana Champaign.

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