Angular momentum and eigenfunctions

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SUMMARY

The discussion focuses on solving a problem related to angular momentum in quantum mechanics, specifically finding the eigenvector |l=1,my=-1> of the operator Ly in terms of the eigenvectors of Lz. The operator Ly is defined as Ly=ihbar[-cos(phi)(-d/dtheta)+cot(theta)sin(phi)(d/dphi)]. The user successfully completed part a but encountered difficulties in part b regarding the function f(theta, phi). Ultimately, the user resolved their query independently.

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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!
 
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Nevermind, I found it. :)
 

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