Generalized uncertainty principle and $D$-dimensional quantum mechanics

Abstract

The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the first order of the GUP parameter.

13 pages, 1 figure, will appear in PRD

References in corpus (3)

• Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity
• GUP and Point Interaction
• Comment on "Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity"

Cited by in corpus (6)

• A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas
• Influence of the dispersion relation on the Unruh effect according to the relativistic Doppler shift method
• Rényi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator
• Quantum speed limit as a sensitive probe of Planck-scale effects
• Aharonov-Bohm-Like Scattering in the Generalized Uncertainty Principle-corrected Quantum Mechanics
• Effects of minimal length on Berry phase and spin-orbit interactions