The Hamiltonian for a certain three-level system is represented by the matrixTwo other obs...

The Hamiltonian for a certain three-level system is represented by the matrix

Two other observables, A and B, are represented by the matrices

where ω, λ, and μ are positive real numbers.

(a) Find the eigenvalues and (normalized) eigenvectors of H, A, and B.

(b) Suppose the system starts out in the generic state

with |c1|2 + |c2|2 + |C3|2 = 1. Find the expectation values (at t = 0) of H, A, and B.

(c) What is  If you measured the energy of this state (at time t), what values might you get, and what is the probability of each? Answer the same questions for A and for B.