Angular momentum and eigenfunctions

[kcasali]

Homework Statement

In this problem all vectors and operators are represented in a system whose basisvectors are the eigenvectors of the operator Lz (the third component of the angular momentum).
a) Find the eigenvector |l=1,my=-1> of Ly in terms of the eigenvectors of Lz.

b) Go from the vector, matrix representation to the function, differential operator representation to find |l=1,my=-1> in function form.

c) Use the definition of Ly and show that the function you found is the Eigenfunction of Ly.

Homework Equations

Ly=ihbar[-cos(phi)(-d/dtheta)+cot(theta)sin(phi)(d/dphi)]

Ly*f(theta, phi) = lambda*f(theta, phi)

The Attempt at a Solution

I got through the part a, with the eigenvectors in the vector, matrix representation, but I'm stuck on part b. I'm not sure what function to use for f(theta, phi), I'm pretty sure I can slog my way through it if I knew that. Any help is much appreciated!

 

[kcasali]

Nevermind, I found it. :)