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 {|ν₁>, |ν₂>}.
(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.