A relativistic model of the isotropic three-dimensional singular oscillator

TL;DR

This paper introduces an exactly solvable relativistic quantum model of the 3D isotropic singular oscillator, deriving wavefunctions and energy spectra that align with non-relativistic limits, advancing theoretical understanding of relativistic quantum systems.

Contribution

The paper presents the first relativistic model of the 3D singular oscillator with explicit solutions in configurational space, including wavefunctions and energy spectra.

Findings

Wavefunctions expressed via continuous dual Hahn polynomials

Energy spectrum derived for the relativistic model

Correct non-relativistic limit demonstrated

Abstract

Exactly solvable model of the quantum isotropic three-dimensional singular oscillator in the relativistic configurational $\vec r$-space is proposed. We have found the radial wavefunctions, which are expressed through the continuous dual Hahn polynomials and energy spectrum for the model under consideration. It is shown that they have the correct non-relativistic limits.