# New solutions to the confluent Heun equation and quasiexact solvability

@article{ElJaick2013NewST, title={New solutions to the confluent Heun equation and quasiexact solvability}, author={L{\'e}a Jaccoud El-Jaick and Bartolomeu D. B. Figueiredo}, journal={arXiv: Mathematical Physics}, year={2013} }

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 stationary Schr\"{o}dinger equation with hyperbolic and trigonometric quasiexactly solvable potentials.

## 6 Citations

Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions

- Mathematics
- 2014

We examine the series expansions of the solutions of the confluent Heun equation in terms of three different sets of the Kummer confluent hypergeometric functions. The coefficients of the expansions…

Appell Hypergeometric Expansions of the Solutions of the General Heun Equation

- Mathematics
- 2014

Starting from a second-order Fuchsian differential equation having five regular singular points, an equation obeyed by a function proportional to the first derivative of the solution of the Heun…

SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS

- MathematicsJournal of Applied Analysis & Computation
- 2019

We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having…

The Floquet Theory of the Two-Level System Revisited

- Mathematics, PhysicsZeitschrift für Naturforschung A
- 2018

Abstract In this article, we reconsider the periodically driven two-level system especially the Rabi problem with linear polarisation. The Floquet theory of this problem can be reduced to its…

Fifteen classes of solutions of the quantum two-state problem in terms of the confluent Heun function

- Physics
- 2014

We derive 15 classes of time-dependent two-state models solvable in terms of the confluent Heun functions. These classes extend over all the known families of three- and two-parametric models…

Integral relations for solutions of the confluent Heun equation

- MathematicsAppl. Math. Comput.
- 2015

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