Semiclassical Analysis of Quasi-Exact Solvability

TL;DR

This paper uses higher-order WKB methods to explore the spectral boundary of quasi-exactly solvable quantum potentials, uncovering key properties that define a new class of semiclassically solvable potentials.

Contribution

It introduces a novel class of semiclassically quasi-exactly solvable potentials based on scaling and factorization properties.

Findings

Identification of scaling and factorization properties

Definition of a new class of semiclassical potentials

Insights into the spectral boundary of solvability

Abstract

Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that are central to quasi-exact solvability. These two properties define a new class of semiclassically quasi-exactly solvable potentials.