1. Not finding help here? Sign up for a free 30min 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!

Commutator relations

  1. Feb 2, 2007 #1
    given that [x,p]=ih, show that if x=x, p has the representation p=-iħ∂/∂x+f(x) where f(x) is an arbitrary function of x
     
  2. jcsd
  3. Feb 3, 2007 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    alisa, you're supposed to show an attempted solution at the problem. That goes for your other threads as well.

    What do you mean " if x=x". x=x by definition.
     
  4. Feb 3, 2007 #3

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    It's the coordinate representation in which the Hilbert space is [itex] L^{2}(\mathbb{R},dx) [/itex]. The "x" operator is realized by a multiplication by "x". She's asked to prove that the most general representation of the momentum operator in this Hilbert space is the one written there.
     
  5. Feb 3, 2007 #4

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    OK, so then it should read something like "If [itex]\hat{x}|\psi>=x|\psi>[/itex]...", right?
     
    Last edited: Feb 3, 2007
  6. Feb 3, 2007 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Exactly. That's the spectral equation, but nonetheless, yes.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Commutator relations
  1. Commutation relations (Replies: 6)

  2. Commutator relations (Replies: 19)

  3. Commutator relations (Replies: 3)

  4. Commutator relations (Replies: 1)

Loading...