Physics NotePublished
Convergence and applications of some solutions of the confluent Heun equation
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
- 29/09/2016
- Description
- We study the convergence of a group of solutions in series of confluent hypergeometric functions for the confluent Heun equation. These solutions are expansions in two-sided infinite series (summation from minus to plus infinity) which are interpreted as a modified version of expansions proposed by Leaver [E. W. Leaver, {J. Math. Phys.} \textbf{27}, 1238 (1986)]. We show that the two-sided solutions yield two nonequivalent groups of one-sided series solutions (summation from zero to plus infinity). In the second place, we find that one-sided solutions of one of these groups can be used to solve an equation which describes a time-dependent two-level system of Quantum Optics. For this problem, in addition to finite-series solutions, we obtain infinite-series wavefunctions which are convergent and bounded for any value of the time $t$, and vanish when $t$ goes to infinity.
- Year
- 2016
- Number
- CBPF-NF-007/16
- Linked to a thesis
- No
- Linked to a grant
- No