1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member


    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

    User Avatar
    Science Advisor
    Homework Helper

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


    Daniel.
     
  7. Feb 3, 2005 #6

    vanesch

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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

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

    cheers,
    Patrick.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Qm problem II
  1. Qm problem (Replies: 9)

  2. QM inverse problem (Replies: 11)

Loading...