The Hydrogen Atom within a pseudo-complex Quantum Mechanics, involving a minimal length

TL;DR

This paper explores a pseudo-complex extension of quantum mechanics applied to the hydrogen atom, revealing energy corrections due to a minimal length scale and setting new bounds on its size using experimental data.

Contribution

It introduces a pseudo-complex framework for quantum mechanics with a minimal length, deriving modified hydrogen atom energies and tighter bounds on the minimal length scale.

Findings

Modified hydrogen energy levels due to minimal length

Upper bounds on minimal length scale from Lamb Shift data

Enhanced restrictions compared to previous estimates

Abstract

The hydrogen atom is investigated, within a pseudo-complex extension of the coordinates and momenta, which introduces a minimal length scale (l) and results into a non-commutative Quantum Mechanics. After resuming the pseudo-complex extension of Quantum Mechanics, the modified energies of the hydrogen atom are deduced, producing corrections of the order of the square of the minimal length scale. Using the Lamb Shift, we obtain an upper boundary for the minimal length scale l, orders of magnitude more restrictive than former estimations.