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Quantum mechanics-projection operator in terms of momentum

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    <x|p^2|x'>=?


    2. Relevant equations
    <x|p|x'>=-ih d/dx dirac delta(x-x')
    I=Integral(dp|p><p|)

    3. The attempt at a solution
    <x|p^2|x'>=<x|p I p|x'>=<x|p Integral(dp)|p><p|p|x'>

    I know that <x|p|x'> = -ih d/dx diracdelta(x-x') so does that mean that <p|p|x'>=-ih d/dx diracdelta(p-x') but that doesn't make sense because the x' and p are different quantities. Maybe just an explanation on the the bra and ket of p vs. the bra and ket of x? I really am lost here...
     
  2. jcsd
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