# A variational formulation for relativistic mechanics, a new interpretation for the Bohr atomic model and some concerning applications

## TL;DR

This paper introduces a variational approach to relativistic quantum mechanics, extending classical mechanics concepts, and explores applications including electromagnetic interactions, chemical reactions, and spin operators.

## Contribution

It develops a novel variational formulation for the Klein-Gordon equation and offers new interpretations for the Bohr model within a relativistic framework.

## Key findings

- Extended classical mechanics to relativistic quantum context
- Modeled electromagnetic field interactions and chemical reactions
- Presented results on relativistic spin operator

## Abstract

This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the quantum mechanics one. For the second part of the text, the definition of normal field and its relation with the wave function concept play a fundamental role in the main results establishment. Among the applications, we include a model with the presence of electromagnetic fields and also the modeling of a chemical reaction. Finally, in the last section, we present some results about the Spin operator in a relativistic context.