Convergence and applications of some solutions of the confluent Heun equation

Léa Jaccoud El-Jaick and Bartolomeu D.B. Figueiredo

Applied Mathematics and Computation, 2016, vol. 284, issue C, 234-259

Abstract: 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 (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.

Keywords: Confluent Heun equation; Spheroidal equation; Three-term recursion; Two-state system (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:284:y:2016:i:c:p:234-259

DOI: 10.1016/j.amc.2016.03.003

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