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Investigations on the minimal-length uncertainty relation

We consider a modified non-relativistic quantum mechanics where the position and momentum operators satisfy a non-standard commutation relation of the form [X<sub>i</sub>, P<sub>j</sub>] = 𝑖ℏ({1 + βP²) + β′P<sub>i</sub>P<sub>j</sub>}. Such a theory incorporates an absolute minimal length, UV/IR mixing and non-commutative position space. The possible representations in terms of differential operators are analyzed and their equivalence to first order is established.

Simple quantum systems, namely the harmonic oscillator, the Coulomb potential and the gravitational well are studied in one of these representations, the pseudo-position one, and results are compared to previously published results. The Coulomb potential is also analyzed by an alternative analytical/numerical method. A constraint of ~ 3 GeV on the scale of the parameters β, β′ is obtained from precision experimental data on the atomic hydrogen energy levels. / Ph. D.

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/26096
Date09 March 2007
CreatorsBenczik, Sandor Zoltan
ContributorsPhysics, Chang, Lay Nam, Tauber, Uwe C., Takeuchi, Tatsu, Haskell, Peter E., Pitt, Mark L.
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
Detected LanguageEnglish
TypeDissertation
Formatapplication/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/
Relationthesis.pdf

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