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Quantum mechanics - Momentum space wave function

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    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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    (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?
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    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?
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    (Original post by suneilr)
    Do you know what the momentum space representation of the x operator is?
    Help?
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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 \hat{x} = x . By the same logic, if we are working in the momentum representation the momentum operator is given by  \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  \hat{x}=i\hbar\frac{d}{dp}

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Updated: April 8, 2012
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