# Off-diagonal Heisenberg matrix element calculation

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

J would like to calculate the off-diagonal matrix element of the Heisenberg spin interaction Hamiltonian between 2 atomic states. **S**_{1}, **S**_{2} are the spin operators with quantum number S, and the states are labelled by m_{1}, m_{2} the z-component quantum numbers of **S**_{1}, **S**_{2} respectively.

**2. Relevant equations**

H = -2J**S**_{1}.**S**_{2}

<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?

http://ift.tt/1lsbSri

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