Van Vleck / Lowdin quasi-degenerate perturbation: block-diagonalise H via Schur-lemma decomposition

Van Vleck / Lowdin quasi-degenerate perturbation theory. Setup: Hamiltonian H = H_0 + V where H_0 has a low-energy subspace P (dim d) separated from a high-energy complement Q by a large gap Delta, but P itself contains quasi-degenerate…