Spectral characteristics for a spherically confined -1/r + br^2 potential

TL;DR

This paper analyzes the spectral properties of a central potential combining Coulomb and harmonic oscillator terms, exploring energy bounds, confinement effects, and providing exact and numerical solutions with implications for physical systems.

Contribution

It offers new analytical and numerical insights into the eigenvalues of the combined potential, including energy bounds and parametric dependencies, under both free and confined conditions.

Findings

Derived exact analytical results for energy spectra.

Identified spectral characteristics through combined analytical and numerical methods.

Discussed experimental implications for free and confined potentials.

Abstract

We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential $V(r)$ is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.