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A problem of momentum representation

  1. Oct 9, 2013 #1
    Given
    [x,p] = i * h-bar,
    prove that
    <p|X|p'> = [i * h-bar / (p' - p)] * δ(p - p').

    I don't understand why commutator matters with this proof?
     
  2. jcsd
  3. Oct 9, 2013 #2
    The commutator tells you what the relationship between p and x is. You are not supposed to use explicit realizations of x or p, but only the commutator.

    Cheers,

    Jazz
     
  4. Oct 9, 2013 #3

    dextercioby

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    This is nonsense. The commutator is defined for the H-space operators, the thing you got to prove is for their distributional extensions.
     
  5. Oct 9, 2013 #4

    Avodyne

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    And what's written is not even true for the distributional extensions.
     
  6. Oct 10, 2013 #5
    Hint: try evaluating <p|[X,p]|p'>, and use the fact (not given, but based on the result this is how |p> is normalized) that <p|p'>= δ(p - p').
     
  7. Oct 10, 2013 #6
    I don't understand how is this a nonsense? I mean we can arrive at second equation (with minor correction) starting from commutation relation and certain assumptions. Can't we?
     
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