542-problem-4 - 1 2 4 2;0 x x ip x x e α π Ψ = h Check...

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Chem. 542 Assignment by Nancy Makri PROBLEM 4 In class we calculated the 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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  • Spring '08
  • Gruebele
  • free particle, time-dependent Schrödinger equation, Nancy Makri, free one-dimensional space, di mensions

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