Spectra generated by a confined softcore Coulomb potential

TL;DR

This paper provides analytic, approximate, and polynomial solutions for the energy levels of a confined softcore Coulomb potential in multiple dimensions, including effects of various confinement types, using the asymptotic iteration method.

Contribution

It introduces new analytic and approximate solutions for confined softcore Coulomb potentials and develops polynomial solutions for related differential equations.

Findings

Derived exact and approximate energy eigenvalues for the potential

Constructed polynomial solutions for linear differential equations

Achieved highly accurate solutions using the asymptotic iteration method

Abstract

Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator potential terms, and also through `hard confinement' by means of an impenetrable spherical box. A byproduct of this work is the construction of polynomial solutions for a number of linear differential equations with polynomial coefficients, along with the necessary and sufficient conditions for the existence of such solutions. Very accurate approximate solutions for the general problem with arbitrary potential parameters are found by use of the asymptotic iteration method.