1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution I suppose to determine if a hamiltonian is rotational invariant, we check if [H(1),L^2], however, I am not sure how to do it if the hamiltonian is operate on a two particle wave function. Is it just to evaluate [S1z Z2 +S2z Z1, L1^2+L2^2]? What is the ground state wave function for this system? I suppose it is A (|0,1,1/2,-1/2> - |0,1,-1/2,1/2>), if you apply S1z, you get 0. It is also true for S2z. I think I am just lost here.