Continued Fraction Methods for Degenerate Perturbation Theory.
Technical rept. Jan-Jul 72,
NATIONAL RESEARCH COUNCIL WASHINGTON D C
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The operator which gives the level shift from the unperturbed to the perturbed system is shown to satisfy a quadratic equation in a Banach space. This quadratic equation is solved using a continued fraction approach and using Newtons method. The asymptotic expansion of the solution using the continued fraction method is shown to be equivalent to the Rayleigh-Schrodinger perturbation expansion. The theory is developed so as to be applicable to the degenerate perturbation problem. Several extensive numerical calculations are reported which show the superiority of the method compared to Rayleigh-Schrodinger perturbation theory, Feenberg perturbation theory and Brillouin-Wigner perturbation theory. Author
- Theoretical Mathematics
- Quantum Theory and Relativity