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Schrödinger equation for two quasi-exactly solvable potentials
Bartolomeu D B Figueiredo
We apply solutions of Heun's general equation to the stationary Schrödinger equation with two quasi-exactly solvable elliptic potentials which depend on a real parameter . We…
Solutions of Heun's general equation and elliptic Darboux equation
Bartolomeu D. B. Figueiredo
New solutions for the elliptic Darboux equation are obtained as particular cases of solutions constructed for Heun's general equation. We consider two groups of power series expans…
New solutions to the confluent Heun equation and quasiexact solvability
Léa Jaccoud El-Jaick, Bartolomeu D. B. Figueiredo
We construct new solutions in series of confluent hypergeometric functions for the confluent Heun equation (CHE). Some of these solutions are applied to the one-dimensional station…
Integral relations for solutions of confluent Heun equations
Léa Jaccoud El-Jaick, Bartolomeu D. B. Figueiredo
Firstly, we construct kernels of integral relations among solutions of the confluent Heun equation (CHE) and its limit, the reduced CHE (RCHE). In both cases we generate additional…
Confluent and Double-Confluent Heun Equations: Convergence of Solutions in Series of Coulomb Wavefunctions
Lea Jaccoud El-Jaick, Bartolomeu D. B. Figueiredo
The Leaver solutions in series of Coulomb wave functions for the confluent Heun equation (CHE) are given by two-sided infinite series, that is, by series where the summation index…
Transformations of Heun's equation and its integral relations
Léa Jaccoud El-Jaick, Bartolomeu D. B. Figueiredo
We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead…