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

by Edgarngg
Tags: angular, eigenfunction, iy or r, momentum, operator, showing
 P: 2 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 $\partial$/$\partial$y - y $\partial$/$\partial$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
 Quote by Edgarngg 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 $\partial$/$\partial$y - y $\partial$/$\partial$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