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The wave equation at infinity

  1. Aug 19, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    The wave equation at plus/minus infinity is zero:

    [tex]\left. {\left| {\psi (x,t)} \right| } \right|_{ - \infty }^\infty= 0[/tex]

    Does this also mean that:

    [tex]
    \left. {\left| {\psi (x,t)} \right|^2} \right|_{ - \infty }^\infty=0
    [/tex]
    ?
     
  2. jcsd
  3. Aug 19, 2008 #2
    no.

    An interpretation of the square of the wavefunction is the probability of finding it somewhere; i.e.[tex]\int^{a}_{b}|\Psi(x,t)|^{2}dx[/tex] is the probability of finding the partical between a and b. you're looking at the probability of finding the partical inbetween +/-[tex]\infty[/tex]. I.e. anywhere.
     
  4. Aug 19, 2008 #3
    I'm not talking about the integral, but only the square of the norm of it. So I am only looking at the probability of finding the particle at exactly + and - infinity.

    Will this equal zero?
     
  5. Aug 19, 2008 #4
    oh, yeah. 0 squared is zero.
     
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