The Salpeter equation and probability current in the relativistic Hamiltonian quantum mechanics

TL;DR

This paper introduces a probability current formalism for relativistic spinless particles using the Salpeter equation, providing exact solutions to demonstrate its validity in Hamiltonian quantum mechanics.

Contribution

It develops a new probability current formalism based on the Salpeter equation, offering an alternative to the Klein-Gordon approach in relativistic quantum mechanics.

Findings

Formalism successfully applied to exact solutions

New solutions to the Salpeter equation are presented

Demonstrates consistency with relativistic quantum principles

Abstract

The probablity current for a quantum spinless relativistic particle is introduced based on the Hamiltonian dynamics approach utilizing the Salpeter equation as an alternative of the Klein-Gordon equation. The correctness of the presented formalism is illustrated by examples of exact solutions to the Salpeter equation including the new ones introduced in this work.