How Do You Calculate Lx and Ly Using Spherical Harmonics in Quantum Mechanics?

[stunner5000pt]

Homework Statement

Obtain the angular momentum operators $L_{x}$ and $L_{y}$ in the basis of functions $Y^{\pm1}_{1}(\theta,phi}$ and [tex]Y^{0}_{1}(\theta,phi}[/itex] in Lz representation<b>2. The attempt at a solution</b><br /> To calculate the matrices for the Lx and Ly operators, do i simply have to take the relevant spherical harmonics and apply Lx and Ly like this<br /> <br /> To form the Lx the terms are given for n'n term of the matrix<br /> <br /> $$(L_{x})_{n'n} = <\psi^{(n'-2)}_{1}|L_{x}|\psi^{(n-2)}_{1}>$$<br /> <br /> from this i can determine the terms of the Lx matrix<br /> similarly for the Ly matrix?<br /> <br /> am i correct? Thanks for any help.[/tex]

 

[Meir Achuz]

It's easier to use the raising and lowering operators L+ and L-.