Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.12.006· OSTI ID:21579874

Ho, Choon-Lin ^[1]

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1. Department of Physics, Tamkang University, Tamsui 251, Taiwan (China)

Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it is also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.

• OSTI ID: 21579874
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 4; Other Information: DOI: 10.1016/j.aop.2010.12.006; PII: S0003-4916(10)00220-4; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DEFORMATION
DIRAC EQUATION
EIGENFUNCTIONS
EXACT SOLUTIONS
FOKKER-PLANCK EQUATION
LAGUERRE POLYNOMIALS
TRANSFORMATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD EQUATIONS
FUNCTIONS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
WAVE EQUATIONS