# Position operator in infinte vector space

1. Sep 30, 2008

### wakko101

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?

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