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 , , and 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...

The Hamiltonian for a certain three-level system is represented by the matrix Two other observables, A and

Question:

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 |S(t)}? 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 observables A and for B.