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Equation problem. How to elimintate t?

  1. Aug 1, 2011 #1
    [itex]\Psi(x,t)=Ae^{-a[(mx^2/h)+i t]}[/itex] (1)

    A and a are positive real constant.

    Use Normalization to get A, the answer says that:

    [itex]1=2|A|^2 \int_0^\inf e^{-2amx^2/h}dx[/itex] (2)

    Can you show me how to do the transform to get the righside of the equation (2)?
     
  2. jcsd
  3. Aug 1, 2011 #2

    HallsofIvy

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    First, you can write the equation as
    [tex]\Psi(x,t)= Ae^{-amx^2/h}e^{ait}[/tex]

    To "normalize" that function means to find A such that the integral of [itex]|\Psi|^2= (\Psi)(\Psi^*)[/itex], the product of [itex]\Psi[/itex] and its complex conjugate, over all "space", is 1. The only "i" is in [itex]e^{ait}[/itex] and, of course, [itex](e^{ait})(e^{-ait})= 1[/itex]. Since this has only one space variable, x, that should be for x from [itex]-\infty[/itex] to [itex]\infty[/itex]. Of course, the function is even in x so you can just integrate from 0 to [itex]\infty[/itex] and then multiply by 2.
     
  4. Aug 1, 2011 #3
    Thank you, HallsofIvy.
    I know it now. In [itex]\Psi^*[/itex] there is a [itex]e^{-ait}[/itex].
    So, [itex]\Psi\Psi^*[/itex] will cause [itex]e^{ait}e^{-ait}=1[/itex], then t is eliminated.

    Thank you so much!
     
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