Computing operator in bra-ket within momentum space

[Void123]

Homework Statement

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

Homework Equations

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.

 

[susskind_leon]

[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]