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Showing that (x+iy)/r is an eigenfunction of the angular momentum operator 
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#1
Mar612, 11:46 PM

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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 


#2
Mar712, 12:38 AM

Sci Advisor
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