An algebraic approach to gravitational quantum mechanics
- URL: http://arxiv.org/abs/2402.17626v1
- Date: Tue, 27 Feb 2024 15:54:18 GMT
- Title: An algebraic approach to gravitational quantum mechanics
- Authors: Won Sang Chung, Georg Junker and Hassan Hassanabadi
- Abstract summary: We study various models of gravitational quantum mechanics using the pseudo or g-calculus.
The spectral properties of a particle bound by an external attractive potential are investigated.
Cases of a box with finite width and infinite walls, an attractive potential well of finite depth and a delta-like 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. Here
we adopt the pseudo or g-calculus to 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 finite width and
infinite walls, an attractive potential well of finite depth and a delta-like
potential are considered.
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