Applications of Lie symmetry analysis to the quantum Brownian motion model.

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Show simple item record Naicker, Viroshan. 2010-08-21T08:10:50Z 2010-08-21T08:10:50Z 2008
dc.description Thesis (M.Sc.) - University of KwaZulu-Natal, Westville, 2008. en_US
dc.description.abstract Lie 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.iso en en_US
dc.subject Lie groups. en_US
dc.subject Differential equations. en_US
dc.subject Theses--Mathematics. en_US
dc.title Applications of Lie symmetry analysis to the quantum Brownian motion model. en_US
dc.type Thesis en_US

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