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Expectation value

  1. Nov 18, 2007 #1
    I'm confused re a particle of energy E < V inside a square potential of width 'a' centered at x = 0 with depth V.

    They give the wavefunction for outside the well as [tex]\Psi(x) = Ae^{k|x|}[/tex] for |x| > a/2

    and [tex]k^2 = -\frac{2ME}{\hbar^2}[/tex] => [tex]k = i\frac{\sqrt{2ME}}{\hbar}[/tex] ?

    I need the probability that the particle is outside the potential well. So I integrate [tex]\int{\Psi(x)\Psi^*(x)dx}[/tex] from a/2 to infinity if I take x to be positive and then multiply by 2 for symmetry?

    But isn't [tex]\Psi(x)^*\Psi(x) = A[/tex]? So my integral is infinity but shouldn't it be 0?
    Last edited: Nov 18, 2007
  2. jcsd
  3. Nov 18, 2007 #2


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    you must integrate from a/2 to infinity, not from 0.

    Because the exponential is real then Psi Psi^* does not give a constant (that only happens for imaginary exponentials)
  4. Nov 18, 2007 #3
    Sorry I meant so say from a/2 to infinity.

    But doesn't k have to have an i in it because k squared is negative?
  5. Nov 18, 2007 #4


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    I am a bit confused by your choice of zero for the potential. You are doing a bound state, right? If you set V =0 outside of the well, then it means E < 0 (but E > -V where I am assuming V is a positive number). Then k is real.
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