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Quantum mechanics - Momentum space wave function

I am asked to find the action of the X operator on the momentum space wave function (see attatchment). I know that the X operator simply multiplies by x, but do I take the x inside the integral, and if so, how?

Thanks
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suneilr
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Original post by samueltaylor123
I am asked to find the action of the X operator on the momentum space wave function (see attatchment). I know that the X operator simply multiplies by x, but do I take the x inside the integral, and if so, how?

Thanks


Do you know what the momentum space representation of the x operator is?
Err, no. I did a similar question with the momentum operator P, in which I just set P acting on the MSWF and manipulated until I got an answer. I thought it was similar?
Original post by suneilr
Do you know what the momentum space representation of the x operator is?


Help?
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suneilr
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Original post by samueltaylor123
Help?


In the position representation, the eigenstates of the position operator correspond to a definite position x, and so we can say the position operator is simply x^=x\hat{x} = x . By the same logic, if we are working in the momentum representation the momentum operator is given by p^=p \hat{p} = p. The commutation relation between x and p is taken as representation independent, and this lead to the position operator in the momentum space representation as being x^=iℏddp \hat{x}=i\hbar\frac{d}{dp}

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