Finite series representation for the bound states of a spiked isotropic oscillator with inverse-quartic singularity

TL;DR

This paper presents an exact finite series solution for the bound states of a 3D spiked isotropic oscillator with inverse-quartic singularity, using the tridiagonal representation approach and Bessel polynomials.

Contribution

It introduces a novel finite series solution for the Schrödinger equation with a singular potential, applicable to all angular momenta.

Findings

Exact finite series solutions obtained for the bound states.

Solutions expressed in terms of Bessel polynomials.

Applicable to all angular momenta.

Abstract

We use the tridiagonal representation approach to obtain an exact solution of the three-dimensional radial Schr\"odinger equation for a spiked oscillator with inverse quartic singularity and for all angular momenta. The solution is a finite series of square integrable functions written in terms of the Bessel polynomial.