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For time t>0, there is a perturbation given by

V(t) = sqrt(3/4)*h_bar*omega* (|2><1| + |1><2|)

After this I need to compute the probability amplitudes. However, my background is in engineering, so I'm unsure how to work with these outer products of two state vectors, or even how this mixing works. If anyone has any hints or links on how to work with these, I would appreciate it very much.

Also, for future reference, do these forums automatically generate LaTeX, or do you import the LaTeX equations I've seen in other posts?