A Study of Modifications to Quantum Mechanics

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dc.contributor.author Lewis, Zachary Evan en_US
dc.date.accessioned 2013-03-06T09:00:16Z
dc.date.available 2013-03-06T09:00:16Z
dc.date.issued 2013-03-05 en_US
dc.identifier.other vt_gsexam:364 en_US
dc.identifier.uri http://hdl.handle.net/10919/19277
dc.description.abstract In this work, the consequences of several modifications to quantum mechanics are examined. These modifications, motivated by string theory, fall into two categories: ones in which the canonical commutation relations between position and momentum are deformed and ones in which the space of states used are vector spaces over Galois fields instead of complex Hilbert spaces. The particular deformation of the canonical commutation relations used leads to a minimum value of the uncertainty in position which is interpreted as a minimum length scale. Both harmonic and anharmonic oscillators are studied in this framework with normalizable, positive energy eigenstates found in both cases. The quantum uncertainty relations and classical counterparts to these states are discussed. Creating modified quantum theories by replacing the Hilbert spaces of canonical quantum mechanics with vector spaces defined over several finite, Galois fields is accomplished. Correlation functions are calculated in these theories and the maximum values are shown to not behave as would be expected by the standard, Bell-like, bounding inequality theorems. The interpretations and implications of these theories are discussed. en_US
dc.format.medium ETD en_US
dc.publisher Virginia Tech en_US
dc.rights The authors of the theses and dissertations are the copyright owners. Virginia Tech's Digital Library and Archives has their permission to store and provide access to these works. en_US
dc.subject Physics en_US
dc.subject Quantum Mechanics en_US
dc.subject Foundations of Quantum Mechanics en_US
dc.title A Study of Modifications to Quantum Mechanics en_US
dc.type Other - Dissertation en_US
dc.contributor.department Physics en_US
dc.description.degree PHD en_US
thesis.degree.name PHD en_US
thesis.degree.level doctoral en_US
thesis.degree.grantor Virginia Polytechnic Institute and State University en_US
thesis.degree.discipline Physics en_US
dc.contributor.committeechair Takeuchi, Tatsu en_US
dc.contributor.committeemember Pitt, Mark L en_US
dc.contributor.committeemember Brown, Ezra A en_US
dc.contributor.committeemember Sharpe, Eric R en_US

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