Year: 2025
Type: article
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 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.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,890
OpenAlex ID: W4410476977