Elementary doublets of bound states of the radial Dirac equation

TL;DR

This paper demonstrates a method to quasi-exactly solve the radial Dirac equation by adapting a technique from non-relativistic quantum mechanics, enhancing understanding of relativistic bound states.

Contribution

It introduces a novel approach to quasi-exactly solve the radial Dirac equation using a substitution similar to the non-relativistic case.

Findings

Method enables quasi-exact solutions of the radial Dirac equation.

Provides insights into relativistic bound state problems.

Bridges techniques between non-relativistic and relativistic quantum mechanics.

Abstract

For non-relativistic Schroedinger equations the lowering of their degree by substitution Psi(r) \to F(r) =Psi'(r) /Psi(r) is known to facilitate our understanding and use of their (incomplete, so called quasi-exact) solvability. We show that and how the radial Dirac relativistic equation may quasi-exactly be solved in similar spirit.