The eigenvalue of the confined potential

TL;DR

This paper derives exact analytical solutions for energy eigenvalues in a 3D confined potential with a linear term, crucial for understanding systems like the Cornell potential, and confirms these solutions with numerical results.

Contribution

It provides the first exact analytical eigenvalues for a linear confined potential in three dimensions, bridging analytical and numerical approaches.

Findings

Analytic eigenvalues match numerical solutions precisely.

Confined potential with linear term modeled accurately.

Insights relevant for systems like the Cornell potential.

Abstract

Analytic solutions for the energy eigenvalues are obtained from a confined potentials of the form $br$ in 3 dimensions. The confinement is effected by linear term which is a very important part in Cornell potential. The analytic eigenvalues and numerical solutions are exactly matched.