Angular momentum operators in quantum mechanics

[myb821]

Homework Statement

H=(J1^2+J2^2)2A+J3^2/2B where J1,2,3 are the angular momentum operators and A and B are just numbers

Homework Equations

The Attempt at a Solution

I rewrote the Hamiltonian as (J^2-Jz^2)/2A + J3^2/2B and got the eigenvalues to be (h^2L(l+1)-h^2m^2)/2A+h^2m^2/2B but i don't know how to find the eigenstates of this hamiltonian help

 

[facenian]

I don't see how you could calculate eigenvalues without using the eigenstates |l,m>