A two-state system is characterized by the Hamiltonian H = H₁₁ |1> <1| + H₂₂|2> <2| + H₁₂ [|1> < 2| + |2> <1|], where H₁₁, H₂₂, and H₁₂ are real numbers with the dimension of energy, and |1> and |2> are eigenkets of some observable (≠ H). Find the energy eigenkets and corresponding energy Eigen values. Make sure that your answer makes good sense for H₁₂ = 0. (You need not solve this problem from scratch. The following fact may be used without proof: (S ∙ n) |n; + > = h/2|n; + >, with |n; + > given by |n; + > = cos β/2 | + > + e ^lα sin β/2 | – 1 >, where β and α are the polar and azimuthal angles, respectively, that characterize n.)