A problem of momentum representation

  • Thread starter fish830617
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  • #1

Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
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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
 
  • #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.
 
  • #4
Avodyne
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And what's written is not even true for the distributional extensions.
 
  • #5
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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?
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').
 
  • #6
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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.
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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