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- Title
Position in Minimal Length Quantum Mechanics.
- Authors
Bosso, Pasquale
- Abstract
Several approaches to quantum gravity imply the presence of a minimal measurable length at high energies. This is in tension with the Heisenberg Uncertainty Principle. Such a contrast is then considered in phenomenological approaches to quantum gravity by introducing a minimal length in quantum mechanics via the Generalized Uncertainty Principle. Several features of the standard theory are affected by such a modification. For example, position eigenstates are no longer included in models of quantum mechanics with a minimal length. Furthermore, while the momentum-space description can still be realized in a relatively straightforward way, the (quasi-)position representation acquires numerous issues. Here, we will review such issues, clarifying aspects regarding models with a minimal length. Finally, we will consider the effects of such models on simple quantum mechanical systems.
- Subjects
QUANTUM gravity; QUANTUM mechanics; PHENOMENOLOGICAL theory (Physics); DE-Broglie waves; HEISENBERG uncertainty principle
- Publication
Universe (2218-1997), 2022, Vol 8, Issue 1, p17
- ISSN
2218-1997
- Publication type
Article
- DOI
10.3390/universe8010017