Generalized dynamical theories in phase space and the hydrogen atom

TL;DR

This paper extends phase-space probabilistic theories to include generalized dynamics, successfully modeling a hydrogen-like system with quantum-like features, and demonstrating the broader applicability of classical and quantum theories within this framework.

Contribution

It introduces a generalized phase-space framework capable of describing nonquantum hydrogen-like systems with stable, discrete energy levels and measurable dynamical effects.

Findings

Modeling of hydrogen-like systems with quantum features

Demonstration of classical and quantum theories as special cases

Prediction of measurable dynamical effects such as Zeeman splitting

Abstract

We show that the phase-space formulation of general probabilistic theories can be extended to include a generalized time-evolution and that it can describe a nonquantum hydrogen-like system which is stable, has discrete energy levels, and includes the Zeeman effect. This allows us to study dynamical effects such as excitations of the hydrogen-like system by a resonant laser and Rutherford scattering. Our construction demonstrates that classical theory and quantum theory can be seen as specific choices of general probabilistic theory in phase space and that other probabilistic theories also lead to measurable predictions.