Asymptotics and monodromy of the algebraic spectrum of quasi-exactly solvable sextic oscillator

TL;DR

This paper investigates the asymptotic behavior, monodromy, and spectral properties of a quasi-exactly solvable sextic oscillator, linking it to classical quartic potentials through theoretical and numerical analysis.

Contribution

It provides new insights into the spectral asymptotics, level crossings, and monodromy of the sextic oscillator, connecting quantum spectral features with classical potentials.

Findings

Asymptotic formulas for the algebraic spectrum are derived.

Identification of level crossing points in the spectrum.

Analysis of monodromy in the complex parameter plane.

Abstract

Below we study theoretically and numerically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic potential, its level crossing points, and its monodromy in the complex plane of its parameter. We also discuss connection between the quasi-exactly solvable sextic and the classical quartic potential.