Write the form of the state vector at times t 0 b what is

Question

Question. Suppose that a given Hamiltonian system has two eigenstates |ε₁> and |ε₂>l where ε_i denotes the cigenstate energy with ε₂ - ε₁> 0. At time t = 0 the state vector for the system has the form

ψ(t = 0) = (|ε₁) + |ε₂)).

(a) Write the form of the state vector at times t > 0.

(b) What is the probability of finding the particle in state |ε₂> as a function of t?