# Generalized Uncertainty Principle and angular momentum

## 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. - Highlights: • Corrections to the angular momentum spectra due to Generalized Uncertainty Principle. • GUP corrections to the hydrogen atom spectrum. • Experimental signatures of GUP, minimum length and Planck scale effects.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22701519

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics

- Additional Journal Information:
- Journal Volume: 383; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; CLEBSCH-GORDAN COEFFICIENTS; CORRECTIONS; QUANTUM GRAVITY; QUANTUM MECHANICS; STERN-GERLACH EXPERIMENT; UNCERTAINTY PRINCIPLE

### Citation Formats

```
Bosso, Pasquale, and Das, Saurya.
```*Generalized Uncertainty Principle and angular momentum*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.06.003.

```
Bosso, Pasquale, & Das, Saurya.
```*Generalized Uncertainty Principle and angular momentum*. United States. doi:10.1016/J.AOP.2017.06.003.

```
Bosso, Pasquale, and Das, Saurya. Tue .
"Generalized Uncertainty Principle and angular momentum". United States. doi:10.1016/J.AOP.2017.06.003.
```

```
@article{osti_22701519,
```

title = {Generalized Uncertainty Principle and angular momentum},

author = {Bosso, Pasquale and Das, Saurya},

abstractNote = {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. - Highlights: • Corrections to the angular momentum spectra due to Generalized Uncertainty Principle. • GUP corrections to the hydrogen atom spectrum. • Experimental signatures of GUP, minimum length and Planck scale effects.},

doi = {10.1016/J.AOP.2017.06.003},

journal = {Annals of Physics},

issn = {0003-4916},

number = ,

volume = 383,

place = {United States},

year = {2017},

month = {8}

}