Effects of a mixed vector-scalar screened Coulomb potential for spinless particles

TL;DR

This paper investigates the bound states of a spinless particle under mixed vector-scalar screened Coulomb potentials in two dimensions, revealing unique solutions including a zero-eigenmode, and extends previous pure potential analyses.

Contribution

It introduces a comprehensive analysis of mixed vector-scalar Coulomb potentials for spinless particles, uncovering novel solutions like zero-eigenmodes in the Klein-Gordon framework.

Findings

Existence of a zero-eigenmode solution.

Analysis of bound states in mixed potentials.

Special cases reduce to pure vector or scalar potentials.

Abstract

The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a bona fide solitary zero-eigenmode solution, are revealed for the Klein-Gordon equation. The cases of pure vector and scalar potentials, already analyzed in previous works, are obtained as particular cases.