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A Study of Modifications to Quantum Mechanics

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dc.contributor.authorLewis, Zacharyen
dc.contributor.committeechairTakeuchi, Tatsuen
dc.contributor.committeememberPitt, Mark L.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.committeememberSharpe, Eric R.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2013-03-06T09:00:16Zen
dc.date.available2013-03-06T09:00:16Zen
dc.date.issued2013-03-05en
dc.description.abstractIn 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
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:364en
dc.identifier.urihttp://hdl.handle.net/10919/19277en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectPhysicsen
dc.subjectQuantum Mechanicsen
dc.subjectFoundations of Quantum Mechanicsen
dc.titleA Study of Modifications to Quantum Mechanicsen
dc.typeDissertationen
thesis.degree.disciplinePhysicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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