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!

Quantum Mechanics Operators

  1. Mar 29, 2014 #1
    1. The problem statement, all variables and given/known data
    Given that [itex] \hat{p} = -i\hbar (\frac{\partial}{\partial r} + \frac{1}{r}) [/itex], show that [itex] \hat{p}^2 = -\frac{\hbar^2}{r^2} \frac{\partial}{\partial r}(r^2 \frac{\partial}{\partial r}) [/itex]

    2. Relevant equations


    3. The attempt at a solution
    I tried [itex]\hat{p}\hat{p} = -\hbar^2((\frac{\partial}{\partial r})^2 + \frac{1}{r} \frac{\partial}{\partial r} + \frac{\partial}{\partial r}\frac{1}{r} +\frac{1}{r^2}) [/itex].

    This gave me [itex] -\hbar^2((\frac{\partial}{\partial r})^2 + \frac{1}{r} \frac{\partial}{\partial r} )[/itex] instead of the 2 / r factor I needed.
    Last edited: Mar 29, 2014
  2. jcsd
  3. Mar 29, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Nope. ##{\partial \over \partial r}{1\over r} ## gives ##{1\over r}{\partial \over \partial r} -{1\over r^2}##
    Remember p is an operator: you have to imagine there is something to the right of it to operate on.
  4. Mar 29, 2014 #3

    I suppose it makes it easier if I had used a test function, and then taken it away.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Quantum Mechanics Operators
  1. Quantum Mechanics (Replies: 2)