New solutions to the confluent Heun equation and quasiexact solvability

TL;DR

This paper develops new series solutions for the confluent Heun equation and applies some to solve specific quasiexactly solvable quantum mechanical potentials.

Contribution

It introduces novel series solutions to the confluent Heun equation and demonstrates their application to certain quasiexactly solvable Schrödinger equations.

Findings

New series solutions for the confluent Heun equation

Application to quasiexactly solvable potentials in quantum mechanics

Enhanced methods for solving specific Schrödinger equations

Abstract

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.