# On the Hydrogen Atom Beyond the Born-Oppenheimer Approximation

## TL;DR

This paper explores a novel signed particle formulation of quantum mechanics to simulate atomic systems beyond the Born-Oppenheimer approximation, demonstrating its potential for accurate quantum chemistry modeling.

## Contribution

It introduces a signed particle approach for simulating complex atomic systems beyond traditional approximations, with applications to the hydrogen atom.

## Key findings

- Successful simulation of quantum tunnelling with signed particles
- Direct simulation of the hydrogen atom as a two-body quantum system
- Indication of the formalism's promise for first-principle quantum chemistry

## Abstract

Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this paper, we comment on the plausibility of simulating atomic systems beyond the Born-Oppenheimer approximation by means of the signed particle formulation of quantum mechanics. First, in order to show the new perspective offered by this new formalism, we provide an example studying quantum tunnelling through a simple Gaussian barrier in terms of the signed particle formulation. Then, we perform a direct simulation of the hydrogen atom as a full quantum two-body system, showing that the formalism can be a very promising tool for first-principle-only quantum chemistry.