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 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&#039;n term of the matrix<br /> <br /> (L_{x})_{n&amp;#039;n} = &amp;lt;\psi^{(n&amp;#039;-2)}_{1}|L_{x}|\psi^{(n-2)}_{1}&amp;gt;<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.

 

[Meir Achuz]

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