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Normalizing: One dimensional wave function

  1. Mar 31, 2013 #1
    1. The problem statement, all variables and given/known data
    At time t = 0 a particle is described by the 1D wave function
    ψ(x,0) = (2α)^1/4 e^-ikx-α
    Verify that this is normalized


    2. Relevant equations
    Er! I have just started this sort of thing, so just a bit confused.
    I think I can do this if there are limits as to where the particle is restricted like the example on this wiki page, but I don't have the restrictions shown in the above question, so how do i do this?


    3. The attempt at a solution

    ψ(x,0) = (2α)^1/4 e^-ikx-α
    To normalize we need to find the value of arbitrary constant, A, from;
    ∫IψI^2 dx = 1 (between ±∞)

    from ψ = A(2α)^1/4 e^-ikx-α
    we have
    ψ^2 = A^2 (2α)^1/4 (e^-ikx-α * e^ikx-α)


    ψ^2 = A^2 (2α)^1/4

    ∫IA^2 (2α)^1/4I dx = 1 (between ±∞)

    . . . . . . . . er . . . . . come to an end.
    Advice or pointer if possible.
    Thank you
     
    Last edited by a moderator: Mar 31, 2013
  2. jcsd
  3. Mar 31, 2013 #2

    vela

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    Your mistake is in the last step: ##e^{-a}e^{-a} = e^{-2a}##.
     
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