Minimal length uncertainty relation and gravitational quantum well
- CWI, P.O. Box 94079, 1090 GB Amsterdam (Netherlands)
The dynamics of a particle in a gravitational quantum well is studied in the context of nonrelativistic quantum mechanics with a particular deformation of a two-dimensional Heisenberg algebra. This deformation yields a new short-distance structure characterized by a finite minimal uncertainty in position measurements, a feature it shares with noncommutative theories. We show that an analytical solution can be found in perturbation and we compare our results to those published recently, where noncommutative geometry at the quantum mechanical level was considered. We find that the perturbations of the gravitational quantum well spectrum in these two approaches have different signatures. We also compare our modified energy spectrum to the results obtained with the GRANIT experiment, where the effects of the Earth's gravitational field on quantum states of ultracold neutrons moving above a mirror are studied. This comparison leads to an upper bound on the minimal length scale induced by the deformed algebra we use. This upper bound is weaker than the one obtained in the context of the hydrogen atom but could still be useful if the deformation parameter of the Heisenberg algebra is not a universal constant but a quantity that depends on the energetic content of the system.
- OSTI ID:
- 20870917
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 74, Issue 3; Other Information: DOI: 10.1103/PhysRevD.74.036002; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ALGEBRA
ANALYTICAL SOLUTION
ATOMS
COMMUTATION RELATIONS
COMPARATIVE EVALUATIONS
DEFORMATION
DISTURBANCES
ELEMENTARY LENGTH
ENERGY SPECTRA
GEOMETRY
GRAVITATIONAL FIELDS
HYDROGEN
QUANTUM MECHANICS
QUANTUM WELLS
TWO-DIMENSIONAL CALCULATIONS
ULTRACOLD NEUTRONS