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Homework Help: Inverse of linear momentum?

  1. Nov 1, 2008 #1
    hi every body!
    I'm looking for inverse of momentum operator in one dimensional problem.I have no idea to solve it!!please help me!
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    so sorry about my bad speaking!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 1, 2008 #2

    tiny-tim

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    Welcome to PF!

    hi ghazal-sh! Welcome to PF! :smile:

    Thankyou for the PM.

    Can you show us the whole problem? :smile:
     
  4. Nov 1, 2008 #3
    thanks for your attention!::smile:
    the problem is just finding inverse of P!
     
  5. Nov 1, 2008 #4

    gabbagabbahey

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    Start by considering the action of the momentum operator [itex]P[/itex] on an arbitrary wavefunction [itex]\psi(x)[/itex]...What is that?
     
  6. Nov 2, 2008 #5
    thanks!how can you reach to 1/p with this approach?
    of course I found the answer.start by calculating expectation value of 1/p in momentum space (so easy)and then use Fourier transform of the wave functions.after so simple calculation you can see that:1/p =integral of dx
     
    Last edited: Nov 2, 2008
  7. Nov 2, 2008 #6

    gabbagabbahey

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    Well, the action of [itex]P[/itex] on [itex]\psi(x)[/itex] is of course just [itex]P\psi(x)=-i\hbar \frac{d}{dx} \psi(x)[/itex]...what do you get when you multiply both sides of this equation by the inverse of P (from the left), [itex]P^{-1}[/itex]?... compare that to the fundamental theorem of calculus and it should be apparent what [itex]P^{-1}[/itex] is.

    P.S. using 1/p to represent the inverse is usually bad notation when dealing with operators.
     
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