Confinement in 3D polynomial oscillators through a generalized pseudospectral method

TL;DR

This paper employs a generalized pseudospectral method to accurately solve the Schrödinger equation for 3D polynomial oscillators under spherical confinement, revealing degeneracy breaking, energy ordering, and reporting new states.

Contribution

It introduces an efficient, accurate approach for solving confined 3D polynomial oscillators, including new state discoveries and detailed analysis of confinement effects.

Findings

Eigenvalues and eigenfunctions computed for various confinement sizes.

Degeneracy breaking and energy ordering analyzed under confinement.

Many new states reported for the first time.

Abstract

Spherical confinement in 3D harmonic, quartic and other higher oscillators of even order is studied. The generalized pseudospectral method is employed for accurate solution of relevant Schr\"odinger equation in an \emph{optimum, non-uniform} radial grid. Eigenvalues, eigenfunctions, position expectation values, radial densities in \emph{low and high-lying} states are presented in case of \emph{small, intermediate and large} confinement radius. The \emph{degeneracy breaking} in confined situation as well as correlation in its \emph{energy ordering} with respect to the respective unconfined counterpart is discussed. For all instances, current results agree excellently with best available literature results. Many new states are reported here for first time. In essence, a simple, efficient method is provided for accurate solution of 3D polynomial potentials enclosed within spherical impenetrable walls.