Variational Solutions to the Brillouin—Wigner Perturbation Differential Equations

Abstract

Variational techniques for the Brillouin—Wigner (BW) perturbation theory, analogous to the Hylleraas and Sinanoğlu principles in Rayleigh—Schrödinger (RS) theory, are derived. A practical method of applying this approach to BW theory, which does not require the knowledge of the exact BW wavefunctions, is discussed. Using this method one obtains an upper bound to the exact total energy for systems in the lowest energy state of a given symmetry. Finally, a convenient matrix method of applying the variational principles is suggested and degenerate BW theory is discussed briefly.