Are we living in Non-Commutative Space? -- revisiting the classic hydrogen atom system

TL;DR

This paper investigates the effects of non-commutative space on the quantum mechanics of the hydrogen atom, highlighting potential corrections to its energy spectrum due to the fuzzy nature of space at microscopic scales.

Contribution

It revisits the hydrogen atom problem within a non-commutative space framework, deriving expected spectral corrections from this novel geometric assumption.

Findings

Predicted measurable energy spectrum shifts due to non-commutative geometry

Provided theoretical foundation for experimental tests of space non-commutativity

Extended quantum mechanical models to include fuzzy space effects

Abstract

Our familiar Newton's laws allow determination of both position and velocity of any object precisely. Early nineteenth century saw the birth of quantum mechanics where all measurements must obey Heisenberg's uncertainty principle. Basically, we cannot simultaneously measure with precision, both position and momentum of particles in the microscopic atomic world. A natural extension will be to assume that space becomes fuzzy as we approach the study of early universe. That is, all the components of position cannot be simultaneously measured with precision. Such a space is called non-commutative space. In this article, we study quantum mechanics of hydrogen atom on such a fuzzy space. Particularly, we highlight expected corrections to the hydrogen atom energy spectrum due to non-commutative space.