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QM: Normalizing a wave function

  1. Aug 20, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    I have a wave function given by

    [tex] \Psi \left( {x,0} \right) = A\frac{x}{a}[/tex]

    I have to normalize it, which is OK. But in the solution to this problem, the teacher uses |A|2 when squaring A. Is there any particular reason for this? I mean, if you square the constant, then why bother with the signs?

    I thought that it maybe because A is a complex constant, but still - I cannot see what difference it would make taking the absolute value of A before squaring.
     
  2. jcsd
  3. Aug 20, 2008 #2

    Redbelly98

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    If A is not real, then |A|2 and A2 are different. Allowing for A to be complex is the only reason I can think of for including the absolute value signs.
     
  4. Aug 20, 2008 #3

    nicksauce

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    For complex numbers, |z|^2 is not the same as z^2. Suppose z = 1 + i. Then |z| = sqrt(2), so |z|^2 = 2. But z^2 = 1 + 2i + i^2 = 2i. |z|^2 always gives a nonnegative real number, which is required to interpret the wave function as a probability density.
     
  5. Aug 20, 2008 #4
    Great, thanks to both of you.
     
  6. Aug 27, 2008 #5
    I have another question related to this.

    When I find the constant A, then am I finding the complex number A or the modulus of the complex number A, |A|?
     
    Last edited: Aug 27, 2008
  7. Aug 27, 2008 #6

    Redbelly98

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    It's |A|.
     
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