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Wave equation question

  1. Nov 16, 2008 #1
    A particle is in a state described by [tex](\frac{mk}{\pi^2 \hbar^{2}})^{1/8}exp(- \frac{1}{2 \hbar} \sqrt{mk}x^{2})exp(-if(t))[/tex]

    When applying separation of variables here, my book ignores the first fraction and sets

    [tex]g(x) = exp(- \frac{1}{2 \hbar} \sqrt{mk}x^{2})[/tex]

    [tex]h(t) = exp(-if(t))[/tex]

    But then [tex]\Psi(x,t) \neq g(x)h(t)[/tex] right?
     
  2. jcsd
  3. Nov 16, 2008 #2

    Hootenanny

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    That is indeed correct.
     
  4. Nov 16, 2008 #3
    The book also says that [tex]p_{op} = -i \sqrt{mk}x exp(\frac{-1}{2 \hbar}\sqrt{mk}x^2)[/tex], so it has ignored the first fraction again. Is this wrong?
     
    Last edited: Nov 16, 2008
  5. Nov 16, 2008 #4

    Hootenanny

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    What is Pop meant to represent?
     
  6. Nov 16, 2008 #5
    The momentum. [tex]p_{op}=-i \hbar \frac{\partial}{\partial x}[/tex]
     
  7. Nov 16, 2008 #6

    Hootenanny

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    Which text is this from? Looking at the wave function, the momentum should be a function of time and should include the nomalisation constant as you say.
     
  8. Nov 16, 2008 #7
    An exam problem at my university, so it oughtn't be wrong.
     
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