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Normalizing a Wave Function

  1. Sep 9, 2013 #1
    1. The problem statement, all variables and given/known data

    ψ(x,t) = Ae^(-λ|x|)e^(-iωt)

    This is a rather long problem so I won't get into the details. I understand how to normalize, and most of the rest of the problem. I also have the solutions manual. I just need an explanation of why this goes to Ae^(-2λ|x|). I can't figure it out.

    2. Relevant equations

    I can't think of any that make sense to use.

    3. The attempt at a solution

    I believe it is because you can add the powers of exponentials, such that e^(x)e^(x) = e^(2x). I do not understand how you can just get rid of the imaginary, angular frequency, or time parts...

    Any explanation would be great.
     
  2. jcsd
  3. Sep 10, 2013 #2

    Dick

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    It's because to normalize you need to integrate ψψ*, the wave function times its complex conjugate. The complex conjugate of e^(-iωt) is e^(iωt). e^(-iωt)*e^(iωt)=e^0=1.
     
  4. Sep 10, 2013 #3
    Ah okay. I had thought it might have something to do with the complex conjugate.

    So for the complex conjugate you just get...

    e^(-λ|x|)*e^(-λ|x|) = e^(-2λ|x|)
     
    Last edited: Sep 10, 2013
  5. Sep 10, 2013 #4

    Dick

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    Sure.
     
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