Suppose that particle 1 (with spin 1) and particle 2 (with spin 1/2) interact via the Hamiltonian operator
H = lambda S1 dot S2 , where lambda is a constant.
Calculate the energy of the state |s,ms> .© BrainMass Inc. brainmass.com June 4, 2020, 12:18 am ad1c9bdddf
You can solve this problem by considering the square of the total spin operator S = S1 + S2. We have:
S^2 = (S1 + S2)^2 = S1^2 + S2^2 + S1 dot S2 + S2 dot S1 = S1^2 + S2^2 + 2 S1 dot S2
In the last line we have used that S1 and S2 commute. This follows from the fact that S1 and S2 act on the spins ...
The expert explains how to diagonalize the inner product of two spin operators