Quantum Mechanics and the Generalized Uncertainty Principle

Abstract

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

8 pages, 3 figures (added references)

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• Generalized uncertainty principles and localization in discrete space
• 30 years in: Quo vadis generalized uncertainty principle?
• Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework
• Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection
• Electroweak Theory with a Minimal Length
• Free particle wavefunction in light of the minimum-length deformed quantum mechanics and some of its phenomenological implications
• Quantum gravity, minimum length and Keplerian orbits
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• Experimental test of uncertainty relations for quantum mechanics on a circle
• Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes
• Dual-phase-modulated plug-and-play measurement-device-independent continuous-variable quantum key distribution
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Quantum theory of the Generalised Uncertainty Principle
• The Mixmaster Universe in a generalized uncertainty principle framework
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• On Generalized Uncertainty Principle
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• Properties of finite Gaussians and the discrete-continuous transition
• Frieden wave function representations via an EPR-Bohm experiment
• Modified clock inequalities and modified black hole lifetime
• Wave Packets in Discrete Quantum Phase Space
• Supersymmetric Field Theory Based on Generalized Uncertainty Principle
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• Quantum probes for universal gravity corrections
• Signature Change by GUP
• Quantized space-time and its influences on some physical problems
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• Particle in a cavity in one-dimensional bandlimited quantum mechanics
• Redshift in a six-dimensional classical Kaluza-Klein type model
• Finite geometry and black hole stability: Embedding discrete space into classical manifolds
• Composable security of unidimensional continuous-variable quantum key distribution
• Properties of a Discrete Quantum Field Theory