Noncommutative gravitational quantum well

Journal Article · Fri Jul 15 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.025010· OSTI ID:20711164

Bertolami, O; Rosa, J G ^[1]; Aragao, C M.L. de; Castorina, P; Zappala, D ^[2]

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1. Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal)
2. Department of Physics, University of Catania and INFN-Sezione di Catania, Citta Universitaria, Via S. Sofia 64, Catania (Italy)

We study noncommutative geometry at the quantum mechanics level by means of a model where noncommutativity of both configuration and momentum spaces is considered. We analyze how this model affects the problem of the two-dimensional gravitational quantum well and use the latest experimental results for the two lowest energy states of neutrons in the Earth's gravitational field to establish an upper bound on the fundamental momentum scale introduced by noncommutativity, namely, {radical}({eta}) < or approx. 1 meV/c, a value that can be improved in the future by up to 3 orders of magnitude. We show that the configuration space noncommutativity has, in leading order, no effect on the problem. We also analyze some features introduced by the model, especially a correction to the presently accepted value of Planck's constant to 1 part in 10{sup 24}.

• OSTI ID: 20711164
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATION RELATIONS
CORRECTIONS
GEOMETRY
GRAVITATIONAL FIELDS
NEUTRONS
QUANTUM MECHANICS
QUANTUM WELLS
TWO-DIMENSIONAL CALCULATIONS