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Qm problem II

  1. Feb 3, 2005 #1
    I am trying to prove that

    [tex] \frac{d\langle p \rangle}{dt} = \langle -\frac{\partial V}{\partial x} \rangle [/tex]

    I am done if I can just prove that

    [tex] \left[ \Psi^*\frac{\partial^2 \Psi}{\partial x^2} \right]_{-\infty}^{\infty} = 0 [/tex]

    [tex] \left[ \frac{\partial \Psi}{\partial x} \frac{\partial \Psi^*}{\partial x} \right]_{-\infty}^{\infty} = 0 [/tex]

    My suggestion is that since [tex]\Psi[/tex] is a wavefunction, it is normalizable and must approach 0 as [tex]x \rightarrow \pm\infty[/tex], and so must its derivatives. I don't know if this argument holds?
     
    Last edited: Feb 3, 2005
  2. jcsd
  3. Feb 3, 2005 #2

    vanesch

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    I would think that's a valid reason, no ?

    cheers,
    Patrick.
     
  4. Feb 3, 2005 #3
    Good luck proving something incorrect! :smile: :biggrin: :tongue2:
     
  5. Feb 3, 2005 #4
    I see your point :) I mean the time derivative, of course.
     
  6. Feb 3, 2005 #5

    dextercioby

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    That's something totally different.It is simply CORRECT...


    Daniel.
     
  7. Feb 3, 2005 #6

    vanesch

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    No, it also excaped me, but of course what is correct is:

    d/dt <p> = <- dV/dx >

    cheers,
    Patrick.
     
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