Klein-Gordon particles in mixed vector-scalar inversely linear potentials

TL;DR

This paper analyzes a spinless particle in a two-dimensional inverse linear potential with mixed vector and scalar components, deriving exact solutions and exploring implications for nonrelativistic hydrogen atom solutions.

Contribution

It provides exact bounded solutions for the Klein-Gordon equation with mixed potentials, ensuring Hermiticity and extending understanding of nonrelativistic limits.

Findings

Exact solutions for the Klein-Gordon equation with mixed potentials.

Nonexistence of even-parity solutions in the nonrelativistic limit.

Support for the nonexistence of certain hydrogen atom solutions.

Abstract

The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the eigenfunctions which ensure that the effective Hamiltonian is Hermitian for all the points of the space. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist.