Consider this problem from the class notes. Solve part (a) of the problem using the density matrix formalism.

(a) The density operator at time t = 0 is ρ(0) = |ν_{e}><ν_{e}|. Write down the density matrix ρ(0) in the eigenbasis
of the Hamiltonian {|ν_{1}>,
|ν_{2}>}.

(b) Write down the matrix of H in this basis and find the matrix of [H,ρ(0)].

(c) Find dρ_{nm}/dt at t = 0 and solve for ρ_{nm}(t).

(d) Find the probability that a measurement at time t will yield an electron
neutrino.