Perturbation Expansions of First Order Eigenvalue Equations in Quantum Mechanics
Abstract
The central field Schrodinger, Klein-Gordon, and Dirac equations can all be written in terms of an independent Riccati equation and a dependent first order linear differential equation. These equations have been expanded for a general excited state with all results expressed in quadrature. The J=0 states of the Breit equation have been shown to reduce to the same form. Applications of this formalism to a large range of both analytical and numerical problems have been considered, including a new variational technique and application to wave function dependent potentials.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1984
- Bibcode:
- 1984PhDT........65R
- Keywords:
-
- RICCATI;
- RICATTI;
- Physics: General