J would like to calculate the off-diagonal matrix element of the Heisenberg spin interaction Hamiltonian between 2 atomic states. S1, S2 are the spin operators with quantum number S, and the states are labelled by m1, m2 the z-component quantum numbers of S1, S2 respectively.
2. Relevant equations
H = -2JS1.S2
<S,S-1|H|S-1,S> = ?
3. The attempt at a solution
I have used the ladder operators for the case S=1/2, but how do we proceed in the general case?