To avoid confusion, I put the symbol "" on top of operators. 1.The Hamiltonian of a two-state system is: Ap = (2 721 ²-21) a) (1 point) Verify that He is Hermitian. b) (3 points) Find eigenvalues of Fo c) (3 points) Find eigenvectors of Ho d) (3 points) Consider the state ) = ( What are the possible outcomes of the experiment in which the energy of the particle in state 1o) is measured? What are the probabilities of the possible outcomes? Hint: It would be easier if you normalize (o) and the two eigenvectors first. e) (2 points) Solve the time-dependent Schrödinger equation: dly) dt ih -=Foly) with the initial condition: (t = 0)) = 1o) = (3), i.e., derive expressions for the components a(1) and b() of the solution 14(t)) = (())

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