On the Laguerre Representation of Coulomb Functions and the Relation to Orthogonal Polynomials
| Autor: | Lorenzo Ugo Ancarani, Gustavo Gasaneo, Jessica A. Del Punta |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Classical orthogonal polynomials
Physics Particle in a spherically symmetric potential symbols.namesake Gegenbauer polynomials Coulomb wave function Discrete orthogonal polynomials Orthogonal polynomials Mathematical analysis Mathematics::Classical Analysis and ODEs Laguerre polynomials symbols Jacobi polynomials |
| DOI: | 10.1016/bs.aiq.2017.06.005 |
| Popis: | We investigate the two-body Coulomb radial problem, providing extensions of known results and establishing a novel connection to orthogonal polynomials. The expansion in Laguerre-type functions of positive energy Coulomb solutions allows one to separate out the radial coordinate from the physical parameters. For the regular Coulomb wave function analytical coefficients are known to be directly connected to Pollaczek polynomials. It turns out that, simultaneously for the attractive and repulsive case, they can also be related to Meixner–Pollaczek polynomials. This allows us to provide a novel interpretation of these coefficients; considering the charge as a variable, we are able to establish orthogonality and completeness properties for these charge functions. We also investigate analytically Laguerre-type expansions of the irregular, incoming and outgoing Coulomb solutions; through a careful limit process we provide the expansion coefficients in closed form. |
| Databáze: | OpenAIRE |
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