# How to get position operator in momentum space?

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1. Sep 27, 2015

### azoroth134

Hi, I wish to get position operator in momentum space using fourier transformation, if I simply start from here,

$$<x>=\int_{-\infty}^{\infty} dx \Psi^* x \Psi$$

I could do the same with the momentum operator, because I had a derivative acting on |psi there, but in this case, How may I get the ih d/dp thing for the position operator, please give some hint

Last edited by a moderator: Sep 27, 2015
2. Sep 27, 2015

### strangerep

Well, since you only wanted a hint...

Express $\Psi(x)$ in terms of its Fourier transform $\tilde\Psi(p)$ .

3. Sep 27, 2015

### azoroth134

I already did that, I just don't know what to do after that, I don't have any derivative to perform on x or p

4. Sep 27, 2015

### blue_leaf77

For a function $f(x)$ and its Fourier transform $F(k)$ (assuming it has one), we have the relation $f'(x) = FT[ikF(k)]$ and the inverse transform $ikF(k) = FT^{-1}[f'(x)]$. Using this how would you write $x\psi(x)$ in momentum space?

5. Sep 27, 2015

### strangerep

Heh, then you should show your work. (Asking only vague questions makes it harder for others to help you constructively.)

6. Sep 29, 2015

### vanhees71

...and do you have to do it with wave functions, or is Dirac notation allowed?