A geometric algebra approach to the hydrogen atom

TL;DR

This paper applies a geometric algebra framework using monogenic functions in 5D spacetime to analyze the hydrogen atom, offering a unified geometric perspective that closely parallels Dirac's equation.

Contribution

It introduces a novel geometric algebra approach to the hydrogen atom, linking monogenic functions in 5D spacetime to quantum solutions similar to Dirac's.

Findings

Solutions resemble Dirac's equation

Provides a geometric interpretation of the hydrogen atom

Unifies physics principles through geometric algebra

Abstract

Monogenic functions in the algebra of 5-dimensional spacetime have been used previously by the author as first principle in different areas of fundamental physics; the paper recovers that principle applying it to the hydrogen atom. The equation that results from the monogenic condition is formally equivalent to Dirac's and so its solutions resemble closely those found in the literature. The use of the monogenic condition as point of departure as not only the advantage of being a unified approach but also provides very strong links with geometry that are completely lost in the usual approach.