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A free particle with mass m has a wavefunction at t = 0 which is given by (x, 0) = Ae~àx² where A and à are real and positive constants. (a) Sketch the wavefunction at t = 0 and determine A using normalization. (b) Determine the wavefunction in k-space $(k). (c) Solve for 4(x, t). (d) Sketch the square of the wavefunction at t = 0, lµ(x,0)|² and at t>0 lp(x,t)l². Comment on what happens to the probability as time increases.

A free particle with mass m has a wavefunction at t = 0 which is given by (x, 0) = Ae~àx² where A and à are real and positive constants. (a) Sketch the wavefunction at t = 0 and determine A using normalization. (b) Determine the wavefunction in k-space $(k). (c) Solve for 4(x, t). (d) Sketch the square of the wavefunction at t = 0, lµ(x,0)|² and at t>0 lp(x,t)l². Comment on what happens to the probability as time increases.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A free particle with mass m has a wavefunction at t = 0 which is given by ¥(x, 0) = Ae~àz where A and à are real and positive constants. (a) Sketch the wavefunction at t = 0 and determine A using normalization. (b) Determine the wavefunction in k-space $(k). (c) Solve for p(x,t). (d) Sketch the square of the wavefunction at t = 0, lµ(x,0)|² and at t>0 Ip(x,t)l². Comment on what happens to the probability as time increases.
Transcribed Image Text:A free particle with mass m has a wavefunction at t = 0 which is given by ¥(x, 0) = Ae~àz where A and à are real and positive constants. (a) Sketch the wavefunction at t = 0 and determine A using normalization. (b) Determine the wavefunction in k-space $(k). (c) Solve for p(x,t). (d) Sketch the square of the wavefunction at t = 0, lµ(x,0)|² and at t>0 Ip(x,t)l². Comment on what happens to the probability as time increases.
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