1. The problem statement, all variables and given/known data Let ( Eo 0 A ) ( 0 E1 0 ) ( A 0 Eo ) be the matrix representation of the Hamiltonian for a three state system with basis states |1> |2> and |3> . If |ψ(0)> = |3> what is |ψ(t)> ?? 2. Relevant equations 3. The attempt at a solution First I need to find the energy eigenstate of the system: H|ψ> = E|ψ> and (Eo 0 A , 0 E1 0, A 0 Eo)T ( <1|ψ> , <2|ψ>, <3|ψ>)T = E( <1|ψ> , <2|ψ>, <3|ψ>)T so I got the equation (Eo - E)(E1 - E)(Eo-E) + A^2(E1-E) = 0 simplify, (Eo - E)^2 (E1 - E) + A^2(E1 - E) = 0 for this equation to be true, then E1 = E .... is this my eigenvalue?? From here, how do I find the energy eigenstate? After that, what should I do to answer the question? I would really appreciate any hint or help... thank you.