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Trouble with normalizing a wave function

  1. Apr 29, 2013 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m is in the state ψ(x,t) = Ae-a[mx2/h-bar)+it]

    Find A

    2. Relevant equations
    I know that to normalize a wave function I should use ∫ψ2 = 1


    3. The attempt at a solution
    The book gives the solution as 1 = 2abs(A)2∫ e-2amx2/h-bar) dx

    My question is where does the "2" factor in front of the A2 come from?
     
  2. jcsd
  3. Apr 29, 2013 #2
    Hmm...could you perhaps provide a little more information on
    (i) the domain of the wavefunction
    (ii) the bounds of that integral
     
  4. Apr 29, 2013 #3
    i) the domain is for all x and t > 0?

    ii) the bounds of the integral are from 0 to ∞
     
  5. Apr 29, 2013 #4
    I think I got it. The solutions manual integrated from 0 to ∞, and multiplied by 2 because of symmetry (to get the -∞ to 0 part)
     
  6. Apr 29, 2013 #5
    Yup, seems like it. It is rather odd of them to do that though; usually we like -∞ to ∞ bounds because they allow us to use the Gaussian integration formula.
     
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