Iteration-Variation Procedures for Quantum-Mechanical Perturbations

Journal Article · Tue Oct 15 04:00:00 EDT 1963 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.1734587· OSTI ID:4686640

Hirschfelder, Joseph O.

The Dalgarno-Lewis procedure was used for obtaining explicit solutions to the perturbation equations. Three basic ideas were exploited: By using the wavefunction through the first order as the zeroth-order wavefunction in a new perturbation calculation, an iteration procedure that converges with surprising rapidity was obtained. After n iterations, the energy is given accurately up to terms of the order of the 2/sup n+1/ power of a perturbation parameter. By varying the proportions of the zeroth- and first-order functions in the wavefunction through the first order, somewhat better energies were obtained and still maintain the ability to iterate. For degenerate and almost degenerate energy levels, the wavefunctions through the first order and the energies through the third order were obtained by solving a finite-ordered secular equation. This procedure is much simpler and less apt to fail than the usual techniques. (auth)

• Research Organization: Univ. of Wisconsin, Madison; Univ. of Florida, Gainesville
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-041600
• OSTI ID: 4686640
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 8 Vol. 39; ISSN JCPSA6; ISSN 0021-9606
• Publisher: American Institute of Physics (AIP)
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ENERGY
ENERGY LEVELS
MATHEMATICS
NUMERICALS
PERTURBATION THEORY
PHYSICS
QUANTUM MECHANICS
VARIATIONAL METHOD
VARIATIONAL PRINCIPLE