# Product eigenstate eigenvalues

1. Jan 21, 2009

### quasar_4

1. The problem statement, all variables and given/known data

What are the eigenvalues of the set of operators (L1^2, L1z, L2^2, L2z) corresponding to the product eigenstate $$\left\langle$$m1 l1 | m2 l2 $$\right\rangle$$?

PS: If you have Liboff's quantum book, this is problem #9.30.

2. Relevant equations

We've also been learning about the Clepsch Gorden coefficients, so they might play a role. I can't figure out enough of the tex on this website to type them (It doesn't seem to like my LaTeX commands, even though I'm usually pretty well-versed on it!).

We also have that | l1l2m1m2> = |l1m1> |l2m2>.

3. The attempt at a solution

I'm very, very confused about these eigenvalues. I am not even sure what the eigenvalue equation looks like. I thought that since | l1l2m1m2> = |l1m1> |l2m2>, maybe the eigenvalues are just the same as | l1l2m1m2> eigenvalues, so that's my current best guess, but I'm not sure. I am confused as to how or if this is related to somehow finding Clebsch-Gordon coefficients. Basically, anything you can tell me will help. In fact, I'd love help just interpeting the problem (I'm not really sure what it is I'm looking for to find these eigenvalues). Any hints? Anyone?