A relativistic model of the $N$-dimensional singular oscillator

TL;DR

This paper introduces an exactly solvable relativistic $N$-dimensional singular oscillator model, deriving wavefunctions, energy spectrum, and symmetry algebra, extending known three-dimensional solutions to higher dimensions.

Contribution

It presents a new relativistic $N$-dimensional model of the singular oscillator, generalizing the three-dimensional case with explicit solutions and symmetry algebra.

Findings

Derived the radial wavefunctions and energy spectrum.

Reduced the $N$-dimensional problem to the three-dimensional case.

Constructed the dynamical symmetry algebra.

Abstract

Exactly solvable $N$-dimensional model of the quantum isotropic singular oscillator in the relativistic configurational $\vec r_N$-space is proposed. It is shown that through the simple substitutions the finite-difference equation for the $N$-dimensional singular oscillator can be reduced to the similar finite-difference equation for the relativistic isotropic three-dimensional singular oscillator. We have found the radial wavefunctions and energy spectrum of the problem and constructed a dynamical symmetry algebra.