Matrix continued fraction solution to the relativistic spin-$0$ Feshbach-Villars equations

TL;DR

This paper introduces a matrix continued fraction approach to solve the relativistic Feshbach-Villars equations for spin-0 particles, providing a new integral equation solution method for bound states in Coulomb-like potentials.

Contribution

It develops a novel matrix continued fraction technique to solve the Feshbach-Villars equations, extending the Coulomb-Sturmian expansion method for relativistic bound-state problems.

Findings

Successful representation of the Feshbach-Villars Coulomb Green's operator as a matrix continued fraction.

Application to bound-state problems in Coulomb plus short-range potentials.

Enhanced computational approach for relativistic quantum equations.

Abstract

The Feshbach-Villars equations, like the Klein-Gordon equation, are relativistic quantum mechanical equations for spin-$0$ particles. We write the Feshbach-Villars equations into an integral equation form and solve them by applying the Coulomb-Sturmian potential separable expansion method. We consider bound-state problems in a Coulomb plus short range potential. The corresponding Feshbach-Villars Coulomb Green's operator is represented by a matrix continued fraction.