Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to get position operator in momentum space?

  1. Sep 27, 2015 #1
    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. jcsd
  3. Sep 27, 2015 #2

    strangerep

    User Avatar
    Science Advisor

    Well, since you only wanted a hint...

    Express ##\Psi(x)## in terms of its Fourier transform ##\tilde\Psi(p)## .
     
  4. Sep 27, 2015 #3
    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
     
  5. Sep 27, 2015 #4

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    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?
     
  6. Sep 27, 2015 #5

    strangerep

    User Avatar
    Science Advisor

    Heh, then you should show your work. (Asking only vague questions makes it harder for others to help you constructively.)
     
  7. Sep 29, 2015 #6

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    ...and do you have to do it with wave functions, or is Dirac notation allowed?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to get position operator in momentum space?
Loading...