(adsbygoogle = window.adsbygoogle || []).push({}); 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

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

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