The purpose of this dissertation is to review the salient features of non-Hermitian quantum
mechanics. An introduction to Hermitian quantum mechanics is included to make
this review as accessible as possible. Attempts at formulating a consistent physical theory
are introduced, before examining non-Hermitian theories' uses as convenient computational
frameworks. Particular emphasis is placed on recent developments in open
quantum systems that utilise non-Hermitian Hamiltonians. Chapter four introduces a
logic that maps a non-Hermitian Hamiltonian onto a non-Hamiltonian algebra that has
a Hermitian Hamiltonian. This was put forward by Sergi, who then goes on to show its
application to a two level system. The time evolution is then derived in terms of the
density matrix model. This system can then be used to analyse di erent types of decay
such as coherence and population di erence. This serves to illustrate the usefulness of
the approach. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/10509 |
| Date | 19 March 2014 |
| Creators | Peacock, Jared L. |
| Contributors | Sergi, Alessandro. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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