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Position operator in infinte vector space

  1. Sep 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Find an expression for <P|X|P> in terms of P(x) defined as <x|P> (and possibly P*(x) )

    2. Relevant equations

    X|P> = x|P>
    Identity operator: integral of |x><x| dx

    3. The attempt at a solution

    Ok...<P|X|P> add the identity
    = Integral [ <P|X|x> <x|P> dx ]
    = Integral [<P|x|x> <x|P> dx ] Here I'm assuming x is a scalar and can be pulled out of the inner product
    = Integral [ x <P|x> <x|P> dx ]
    = Integral [ x <x|P>* <x|P> dx ]
    = Integral [ x P*(x) P(x) dx ]

    Does this look right?
  2. jcsd
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