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Computing operator in bra-ket within momentum space

  1. Oct 13, 2011 #1
    1. The problem statement, all variables and given/known data

    [itex]<e^{ip'x}|x^{2}|e^{ipx}>[/itex]


    2. Relevant equations






    3. The attempt at a solution

    Its pretty obvious that its difficult to integrate in position-space, so I rewrite x in momentum space (i.e. the second-order differential operator with respect to p).

    If that is the case, is this correct (which is the part I'm not sure about):

    [itex]C \int^{-\infty}_{-\infty} e^{ip'x}\frac{∂^{2}}{∂p^{2}}e^{ipx} dp[/itex]

    (hbar is absorbed into the constant on the side)

    Or do I have to fourier transform [itex]e^{ip'x}[/itex] and [itex]e^{ipx}[/itex]?

    Thanks.
     
  2. jcsd
  3. Oct 13, 2011 #2
    [itex]e^{ipx}[/itex] is the wavefunction given in position space, so if you want to integrate in momentum space, you need to express the wavefunctions in momentum space as well, which should be [itex]\delta(p_1-p)[/itex]
     
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