Study of a class of non-polynomial oscillator potentials

TL;DR

This paper introduces a variational method to accurately estimate eigenenergies of a non-polynomial oscillator potential in multiple dimensions, providing bounds and exact solutions for comparison.

Contribution

It develops a novel variational approach for non-polynomial potentials and derives an infinite set of exact solutions for benchmarking.

Findings

The variational bounds are highly accurate compared to previous results.

An infinite set of exact solutions is obtained for the potential.

The method applies to arbitrary dimensions N>1.

Abstract

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.