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Consider a two object spin system. For t>0 the Hamiltonian is given as:

H= 4*LAPLACE/h_^2 * S_1*S_2

The initial state is given as |+->. I need to calculate the probabilities of finding the system in one of the four possible states (|++>,|+->,|-->,|-+>)

a) by solving the problem exactly

b) by using the time dependent perturbation theory (H being the perturbation)

Perhaps somebody could give me a hint? I could write S_1*S_2 as S_1z*S_2z + 0.5 (S_1+*S_2- + S_1-*S_2+) to use the known eigen-value equations for S_z.

Thanks in advance.

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# Spin System

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