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Unformatted text preview: Homework #1  Probability distribution Due Sept. 16, 2011 at 11:35, in class Tami PeregBarnea 1. Griffiths 1.4+: At time t = 0 a particle is represented by the wavefunction: Ψ( x, 0) = A x a if 0 ≤ x ≤ a A b x b a if a ≤ x ≤ b otherwise (1) where a and b are constants. (a) Normalize the wavefunction. (b) Sketch Ψ( x, 0) as a function of x . (c) Where is the particle most likely to be found at t = 0? (d)What is the probability to find the particle to the left of a ? check your result in the limiting cases b = a and b = 2 a , does your result make sense? (e)What is the expectation value of x ? (f)What is the variance of x ? 2. Griffiths 1.5+: Consider the wavefunction Ψ( x,t ) = Ae λ  x  e iωt (2) where A,λ and ω are real. (a) Normalize the wavefunction. (b) Calculate the expectation value of x and x 2 . (c) What is the standard deviation, σ of x ?...
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This note was uploaded on 03/21/2012 for the course PH 357 taught by Professor Tamiperegbarnea during the Fall '10 term at McGill.
 Fall '10
 TamiPeregBarnea
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