Publication: Laguerre polynomials in a relativistic quantum-statistical model
Loading...
Identifiers
Publication date
1996
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad Carlos III de Madrid, Departamento de Matemáticas
Impact
Export
Abstract
The main aim of this work is to find analytical expressions for the eigenvalues and eigenfunctions corresponding to Dirac equation, for hot and dense matter. It is shown that the Laguerre polynomials depending on the effective charge are solutions for self-consistent fields. To determine the screening constant and affective charge we introduce and minimize a functional. These formulas are accurate for machine calculation of bound-bound, bound-free and free-free transitions, including large values of principal quantum numbers. Hence these expressions would be in accordance with quantum-statistical results based on more sophisticated calculations. Comparison with the solutions of the Schrödinger equation for different substancies are discussed.
Description
13 pages, 2 figures.-- MSC2000 codes: 33C45, 82B10, 42C05, 81Q05.-- Contributed to: International Workshop on Orthogonal Polynomials in Mathematical Physics (IWOP'96, in honour of Professor André Ronveaux, Leganés, Spain, June 24-26, 1996).
MR#: MR1466766 (98i:33009)
Zbl#: Zbl 0951.33009
MR#: MR1466766 (98i:33009)
Zbl#: Zbl 0951.33009
Keywords
Dirac equation, Orthogonal polynomials, Quantum-statistical mechanics
Bibliographic citation
Proceedings of the International Workshop on Orthogonal Polynomials in Mathematical Physics (IWOP'96), M. Alfaro et al (eds), p. 23-35