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dc.contributor.authorNaicker, Viroshan.
dc.date.accessioned2010-08-21T08:10:50Z
dc.date.available2010-08-21T08:10:50Z
dc.date.issued2008
dc.identifier.urihttp://hdl.handle.net/10413/455
dc.descriptionThesis (M.Sc.) - University of KwaZulu-Natal, Westville, 2008.en_US
dc.description.abstractLie symmetry group methods provide a useful tool for the analysis of differential equations in a variety of areas in physics and applied mathematics. The nature of symmetry is that it provides information on properties which remain invariant under transformation. In differential equations this invariance provides a route toward complete integrations, reductions, linearisations and analytical solutions which can evade standard techniques of analysis. In this thesis we study two problems in quantum mechanics from a symmetry perspective: We consider for pedagogical purposes the linear time dependent Schrodinger equation in a potential and provide a symmetry analysis of the resulting equations. Thereafter, as an original contribution, we study the group theoretic properties of the density matrix equation for the quantum Brownian motion of a free particle interacting with a bath of harmonic oscillators. We provide a number of canonical reductions of the system to equations of reduced dimensionality as well as several complete integrations.en_US
dc.language.isoenen_US
dc.subjectLie groups.en_US
dc.subjectDifferential equations.en_US
dc.subjectTheses--Mathematics.en_US
dc.titleApplications of Lie symmetry analysis to the quantum Brownian motion model.en_US
dc.typeThesisen_US


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