https://doi.org/10.1140/epjp/s13360-025-06335-8
Regular Article
An algebraic approach to gravitational quantum mechanics
1
Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University, 660-701, Jinju, Korea
2
Institut für Theoretische Physik I, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany
3
European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748, Garching, Germany
4
Departamento de Física Teórica, Atómica y Optica and Laboratory for Disruptive Interdisciplinary Science (LaDIS), Universidad de Valladolid, 47011, Valladolid, Spain
5
Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czechia
a georg.junker@fau.de, gjunker@eso.org
Received:
12
December
2024
Accepted:
15
April
2025
Published online:
18
May
2025
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of Heisenberg’s algebra resulting in a generalised uncertainty principle and constitute what is called gravitational quantum mechanics. Utilising the position representation of this deformed algebra, we study various models of gravitational quantum mechanics. The free time evolution of a Gaussian wave packet is investigated as well as the spectral properties of a particle bound by an external attractive potential. Here the cases of a box with infinite walls and an attractive potential well of finite depth are considered.
© The Author(s) 2025
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