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!

Homework Help: Operator Theory Problem on Momentum Operator (QM)

  1. Jun 29, 2013 #1
    1. The problem statement, all variables and given/known data

    Given the operators [itex]\hat{x}=x\cdot[/itex] and [itex]\hat{p}=-i\hbar \frac{d}{dx}[/itex], prove that:

    [itex][\hat{x}, g(\hat{p})]=i\hbar \frac{dg}{d\hat p}[/itex]

    2. Relevant equations


    3. The attempt at a solution

    I have very little idea on how to begin this problem, but I don't want a solution, I simply want a hint in the right direction.

    Thanks, mates.
    Last edited: Jun 29, 2013
  2. jcsd
  3. Jun 29, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Expand ##g(p)## in a power series. What's ##[x,p^n]##?
  4. Jun 29, 2013 #3
    Actually, I realized it was even easier than that, but thank you!

    Consider the case in momentum-space rather than position-space, and this reduces nicely using elementary operations.
  5. Jun 29, 2013 #4


    User Avatar
    Science Advisor
    Homework Helper

    Sure, that works also. x is a differentiation operator in p space.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted