This thesis studies deformation quantization and its application to contact interactions
and systems with dissipation. We consider the subtleties related to quantization
when contact interactions and boundaries are present. We exploit the idea that discontinuous
potentials are idealizations that should be realized as limits of smooth
potentials. The Wigner functions are found for the Morse potential and in the proper
limit they reduce to the Wigner functions for the infinite wall, for the most general
(Robin) boundary conditions. This is possible for a very limited subset of the
values of the parameters -- so-called fine tuning is necessary. It explains why Dirichlet
boundary conditions are used predominantly. Secondly, we consider deformation
quantization in relation to dissipative phenomena. For the damped harmonic oscillator
we study a method using a modified noncommutative star product. Within this
framework we resolve the non-reality problem with the Wigner function and correct
the classical limit. / iii, 188 leaves ; 29 cm
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:ALU.w.uleth.ca/dspace#10133/2490 |
| Date | January 2010 |
| Creators | Belchev, Borislav Stefanov, University of Lethbridge. Faculty of Arts and Science |
| Contributors | Walton, Mark A |
| Publisher | Lethbridge, Alta. : University of Lethbridge, Dept. of Physics and Astronomy, c2010, Arts and Science, Department of Physics and Astronomy |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | Thesis (University of Lethbridge. Faculty of Arts and Science) |
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