Applications of Lie symmetry analysis to the quantum Brownian motion model.
| dc.contributor.author | Naicker, Viroshan. | |
| dc.date.accessioned | 2010-08-21T08:10:50Z | |
| dc.date.available | 2010-08-21T08:10:50Z | |
| dc.date.issued | 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.identifier.uri | http://hdl.handle.net/10413/455 | |
| 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 |