Physics NotePublished
Confluent Heun Equations: Convergence of Solutions in Series of Coulomb Wavefunctions
Léa Jaccoud El-Jaick; Bartolomeu Donatila Bonorino Figueiredo
Publication details
- Authors
- Léa Jaccoud El-Jaick; Bartolomeu Donatila Bonorino Figueiredo
- Type
- Physics Note
- Status
- Published
- Publication date
- 11/12/2012
- Description
- The Leaver solutions in series of Coulomb wave functions for the confluent Heun equation are given by two-sided infinite series, that is, by series where the summation index $n$ runs from minus to plus infinity [E. W. Leaver, {J. Math. Phys.} \textbf{27}, 1238 (1986)]. First we show that, in contrast to the D'Alembert test, under certain conditions the Raabe test assures that the domains of convergence of these solutions include an additional singular point. We also consider solutions for a limit of the confluent Heun equation. For both equations, new solutions are generated by transformations of variables. Finally we discuss the time dependence of the Klein-Gordon equation in two cosmological models and the spatial dependence of the Schr\"{o}dinger equation to a family of quasi-exactly solvable potentials. For a subfamily of these potentials we obtain infinite-series solutions which converge and are bounded for all values of the independent variable, in opposition to a common belief.
- Year
- 2012
- Number
- CBPF-NF-015/12
- Linked to a thesis
- No
- Linked to a grant
- No