Propagators of singular anharmonic oscillators with quasi-equidistant spectra

TL;DR

This paper derives analytical propagators for singular anharmonic oscillators with quasi-equidistant spectra using Darboux transformations and the image method, exploring multi-well potentials and magnetic field configurations.

Contribution

It introduces explicit propagator formulas for singular oscillators with complex potentials, expanding analytical tools for quantum systems with singularities.

Findings

Explicit propagators for two-well and three-well potentials

Identification of magnetic field configurations related to these potentials

Application of the image method to formal singular propagators

Abstract

Darboux transformations of the singular harmonic oscillator are considered. Analytical expressions for the propagators are obtained, using the image method applied to formal singular propagators. Two-well and three-well families of potentials and the corresponding propagators are presented. Axially symmetric magnetic field configurations corresponding to these potentials have been identified.