Novel quasi-exactly solvable models with anharmonic singular potentials

TL;DR

This paper introduces new quasi-exactly solvable quantum models with complex anharmonic potentials, providing exact solutions for energies and wave functions using the functional Bethe ansatz method.

Contribution

It presents novel solvable models with high-order anharmonic potentials and derives explicit solutions and parameter conditions analytically.

Findings

Exact energy and wave function solutions for new potentials

Analytical expressions for potential parameters

Application of the functional Bethe ansatz method

Abstract

We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly via the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of a set of algebraic equations.