# Inverse of linear momentum?

1. Nov 1, 2008

### ghazal-sh

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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1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 1, 2008

### tiny-tim

Welcome to PF!

hi ghazal-sh! Welcome to PF!

Thankyou for the PM.

Can you show us the whole problem?

3. Nov 1, 2008

### ghazal-sh

thanks for your attention!:
the problem is just finding inverse of P!

4. Nov 1, 2008

### gabbagabbahey

Start by considering the action of the momentum operator $P$ on an arbitrary wavefunction $\psi(x)$...What is that?

5. Nov 2, 2008

### ghazal-sh

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
6. Nov 2, 2008

### gabbagabbahey

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

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