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.

arXiv comment13 pages, 1 figure, will appear in PRD

References in corpus (12)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• A Generalized Uncertainty Principle in Quantum Gravity
• Loop Quantum Gravity
• Quantum Gravity: a Progress Report
• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• Path integral treatment of two- and three-dimensional delta-function potentials and application to spin-1/2 Aharonov-Bohm problem
• Path Integral for non-relativistic Generalized Uncertainty Principle corrected Hamiltonian
• 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"
• Equivalence of renormalization with self-adjoint extension in Green's function formalism

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• 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