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dc.contributor.authorLewis, Zachary Evanen_US
dc.date.accessioned2013-03-06T09:00:16Z
dc.date.available2013-03-06T09:00:16Z
dc.date.issued2013-03-05en_US
dc.identifier.othervt_gsexam:364en_US
dc.identifier.urihttp://hdl.handle.net/10919/19277
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_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThe 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.subjectPhysicsen_US
dc.subjectQuantum Mechanicsen_US
dc.subjectFoundations of Quantum Mechanicsen_US
dc.titleA Study of Modifications to Quantum Mechanicsen_US
dc.typeOther - Dissertationen_US
dc.contributor.departmentPhysicsen_US
dc.description.degreePHDen_US
thesis.degree.namePHDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplinePhysicsen_US
dc.contributor.committeechairTakeuchi, Tatsuen_US
dc.contributor.committeememberPitt, Mark Len_US
dc.contributor.committeememberBrown, Ezra Aen_US
dc.contributor.committeememberSharpe, Eric Ren_US


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