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QM: Normalized wavefunctions

  1. Mar 20, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    If I have two normalized wavefunctions f and g, will their product fg also be a normalized wavefunction?

    Thanks in advance.

    Best regards,
    Niles.
     
  2. jcsd
  3. Mar 20, 2009 #2

    CompuChip

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    Nope.
    Consider this wavefunction from Wikipedia :)

    [tex]\psi(x, t) = \begin{cases} \frac{1}{\sqrt{L}} \exp\left[ i(kx - \omega t) \right] & \text{ if } 0 \le x \le L \\ 0 & \text{otherwise} \end{cases}[/tex]
    (this is actually the wavefunction of a particle in a 1-D box of size L).

    Now you can check that [itex]\psi[/itex] is normalized (by the 1/L^(1/2) in front) and take [itex]f = g = \psi[/itex]
     
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