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Sharp values of wavefunction in polar coordinates

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider the function in polar coordinates

    ψ(r,θ,[itex]\phi[/itex]) = R(r)sinθ[itex]e^{i\phi}[/itex]

    Show by direct calculation that ψ returns sharp values of the magnitude and z-component of the orbital angular momentum for any radial function R(r). What are these sharp values?

    3. The attempt at a solution

    I -think- for [itex]L_{z}[/itex] to be sharp, you have to impose the eigenfunction condition

    [itex]-i\hbar \frac{dψ}{d\phi} = L_{z}ψ[/itex]

    which means that the radial function R(r) would cancel with itself if you were to rearrange the above for [itex]L_{z}[/itex]. However I could have completely the wrong idea here.
  2. jcsd
  3. Sep 25, 2013 #2


    User Avatar

    Staff: Mentor

    How about calculating the expectation values corresponding to "the magnitude and z-component of the orbital angular momentum "?
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