On the wave mechanics of a particle in two different impenetrable spherical cavities

TL;DR

This paper critically analyzes the wave mechanics of a particle in impenetrable spherical cavities, examining the effects of a central scattering potential and its implications for energy eigenvalues.

Contribution

It introduces a nuanced analysis of energy eigenvalues considering a central scattering potential, refining existing models of particles in spherical cavities.

Findings

Modified energy eigenvalues due to scattering potential

Insights into particle behavior in confined spherical geometries

Refinement of quantum confinement models

Abstract

Wave mechanics of a particle in an impenetrable spherical cavity with and without a hard core scattering potential of size $\epsilon$ ($\epsilon$ $\to$ 0) at its center is critically analyzed. It makes marginal but important modifications in our present understanding of the energy eigenvalues of such particles.