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Homework Help: Commutator relations

  1. Feb 2, 2007 #1

    alisa

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    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
     
    alisa, Feb 2, 2007
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  3. Feb 3, 2007 #2

    Tom Mattson

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    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.
     
    Tom Mattson, Feb 3, 2007
  4. Feb 3, 2007 #3

    dextercioby

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    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.
     
    dextercioby, Feb 3, 2007
  5. Feb 3, 2007 #4

    Tom Mattson

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

    dextercioby

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    Exactly. That's the spectral equation, but nonetheless, yes.
     
    dextercioby, Feb 3, 2007
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