1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivation of momentum operator / origin of -ih d/dx

  1. Aug 13, 2011 #1
    1. The problem statement, all variables and given/known data
    In the derivation of the momentum operator: Why is this equal?


    2. Relevant equations
    [PLAIN]http://img268.imageshack.us/img268/4575/momentumoperatorderivat.png [Broken]


    3. The attempt at a solution
    I thought maybe the integral is executed, but the integral sign stays.
    One p vanishes, the momentum operator itself shows up.
    You would really expect this in a derivation of p, but dp stays.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Aug 13, 2011 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    There's two steps in there. First, you can write
    [tex]p \exp\left(\frac{ipx}{\hbar}\right) = \frac{\hbar}{i}\frac{\partial}{\partial x}\exp\left(\frac{ipx}{\hbar}\right)[/tex]
    Then you interchange the order of integration and differentiation.
     
  4. Aug 13, 2011 #3
    Now I see it. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivation of momentum operator / origin of -ih d/dx
  1. Momentum in 2-D (Replies: 1)

  2. 2-d momentum collision (Replies: 2)

Loading...