Ultrarelativistic bound states in the shallow spherical well

TL;DR

This paper investigates the properties of bound states in a 3D ultrarelativistic shallow spherical well, identifying energy thresholds and eigenfunctions, enhancing understanding of massless quantum systems.

Contribution

It provides approximate eigenvalues and shapes of bound states in a massless, ultrarelativistic quantum well, including thresholds for state existence.

Findings

Existence thresholds for bound states identified

Eigenfunctions approximated for radial and non-radial states

Insights into energy storage in massless quantum systems

Abstract

We determine approximate eigenvalues and eigenfunctions shapes for bound states in the $3D$ shallow spherical ultrarelativistic well. Existence thresholds for the ground state and first excited states are identified, both in the purely radial and orbitally nontrivial cases. This contributes to an understanding of how energy may be stored or accumulated in the form of bound states of Schr\"odinger - type quantum systems that are devoid of any mass.