Generalized Uncertainty Principle and Angular Momentum

TL;DR

This paper explores how the Generalized Uncertainty Principle, inspired by quantum gravity models, modifies angular momentum theory in quantum mechanics, affecting eigenvalues, spectra, and multi-particle systems.

Contribution

It provides explicit calculations of Planck scale corrections to angular momentum eigenvalues, spectra, and coefficients, extending quantum mechanics with GUP effects.

Findings

Planck scale corrections to angular momentum eigenvalues

Modified hydrogen atom spectrum due to GUP

Altered Clebsch-Gordan coefficients and multi-particle effects

Abstract

Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the theory of angular momentum in Quantum Mechanics. In particular, we compute Planck scale corrections to angular momentum eigenvalues, the Hydrogen atom spectrum, the Stern-Gerlach experiment and the Clebsch-Gordan coefficients. We also examine effects of the Generalized Uncertainty Principle on multi-particle systems.