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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!
    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


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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


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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


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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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