VARIATIONAL SOLUTIONS TO THE BRILLOUIN-WIGNER PERTURBATION DIFFERENTIAL EQUATIONS,
Abstract
The usual Brillouin-Wigner (BW) perturbation theory series expansions for the energy and wave function of a perturbed system are replaced by a set of perturbation differential equations. Thus it seems probable that many of the developments of Rayleigh-Schrodinger (RS) perturbation theory which depend largely on the RS perturbation differential equations should carry over to BW theory. A variational method, analogous to the Hylleraas principle in RS6theory, is derived which can be used to obtain approximate solutions to the n-th order BW perturbation equation for systems in the lowest energy state of a given symmetry. The BW energy to (2n)-th order obtained in this manner is an upper bound to the exact BW energy to (2n)-th order if the (n-1)-th order wave function is known exactly. This is usually true for n=1 only. It is shown, however, that these variational techniques give an upper bound to the total energy even if the (n-1)-th order BW wave function is unknown. A convenient matrix method of applying the variational principles is suggested and a method of using this formulation of BW perturbation theory is discussed formally. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 14, 1963
- Accession Number
- AD0424633
Entities
People
- William J. Meath
Organizations
- University of Wisconsin–Madison