Physics · Quantum Mechanics

A two-level quantum system has the Hamiltonian H = ℏω0 &begin;pmatrix& rang; 0 & 1 \ 1 & 0 &end;pmatrix& rang;. At t = 0, the system is in the state |ψ(0)⟩ = &begin;pmatrix& rang; 1 \ 0 &end;pmatrix& rang;. What is the earliest time t > 0 at which a measurement of σz = &begin;pmatrix& rang; 1 & 0 \ 0 & -1 &end;pmatrix& rang; will yield the value -1 with probability one?