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Showing that (x+iy)/r is an eigenfunction of the angular momentum operator

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data
    I know that,if (operator)(function)=(value)(samefunction)
    that function is said to be eigenfunction of the operator.
    in this case i need to show this function to be eigenfunction of the Lz angular momentum:


    2. Relevant equations
    function:
    ψ=(x+iy)/r
    operator:
    Lz= (h bar)/i (x [itex]\partial[/itex]/[itex]\partial[/itex]y - y [itex]\partial[/itex]/[itex]\partial[/itex]x)


    3. The attempt at a solution
    My question is how do i treat "r", do i have to change to polar coordinates? or is it possible to do it like this.
    i know that i have to apply the operator over the function, and that is (h bar/i) (x(partial derivative for y)- y(partial der for x)) and then see if i get the same function multiplied by an eigenvalue.
    the problem i have is that i dont know how to treat that function, since i see an "r" there. So when d/dx "r" and "y" would be constant, and that doesnt make sense to me.
    Thank you very much
     
    Last edited: Mar 7, 2012
  2. jcsd
  3. Mar 7, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    r=sqrt(x^2+y^2), isn't it?
     
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