Show that the linear combinations of states that diagonalize the Hamiltonian of the hydrogen molecule ion are given by (12.71). Verify that these states are properly normalized and that the corresponding energy expectation values are given by (12.72). Note: If ∣ψ⟩ is not normalized, then ⟨E⟩=⟨ψ∣H^∣ψ⟩/⟨ψ∣ψ⟩.