An algebraic approach to gravitational quantum mechanics

• URL: http://arxiv.org/abs/2402.17626v2
• Date: Fri, 6 Sep 2024 10:39:29 GMT
• Title: An algebraic approach to gravitational quantum mechanics
• Authors: Won Sang Chung, Georg Junker, Hassan Hassanabadi,
• Abstract summary: We study various models of gravitational quantum mechanics. The free time evolution of a Gaussian wave packet is investigated. The spectral properties of a particle bound by an external attractive potential are considered.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 generalized uncertainty principle and constitute what is called gravitational quantum mechanics. Utilizing 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.

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