dc.contributor.advisor | Digernes, Trond | |
dc.contributor.advisor | Landstad, Magnus Brostrup | |
dc.contributor.author | Bakken, Erik Makino | |
dc.date.accessioned | 2016-08-19T07:32:16Z | |
dc.date.available | 2016-08-19T07:32:16Z | |
dc.date.issued | 2016 | |
dc.identifier.isbn | 978-82-326-1763-0 | |
dc.identifier.issn | 1503-8181 | |
dc.identifier.uri | http://hdl.handle.net/11250/2399941 | |
dc.description.abstract | Approximation of quantum systems by nite dimensional quantum systems
goes back to the foundation of quantum mechanics. Finite dimensional
quantum systems were considered by Hermann Weyl, and were considered
in much detail by Julian Schwinger. Our main interest is to approximate
the spectrum of Hamiltonians by the spectrum of nite dimensional Hamiltonians.
In a paper from 1994 by Digernes, Varadarajan and Varadhan, an
approximation theorem was proved for a wide class of Hamiltonians.
The main goal of this thesis is to generalize these results to di erent
settings. One of the cases we investigate is the Hamiltonian with Coulomb
potential. We will also generalize these results to the more unconventional
setting of non-Archimedean quantum mechanics. Quantum mechanics over
p-adic numbers was introduced by Volovich in 1987. Quantum mechanics in
the p-adic setting is the most studied non-Archimedean model in quantum
mechanics, and it has been generalized to local elds which will be our
setting for non-Archimedean physics. | nb_NO |
dc.language.iso | eng | nb_NO |
dc.publisher | NTNU | nb_NO |
dc.relation.ispartofseries | Doctoral thesis at NTNU;2016:212 | |
dc.title | Finite Approximations of Quantum Systems in a Non-Archimedean and Archimedean Setting | nb_NO |
dc.type | Doctoral thesis | nb_NO |
dc.subject.nsi | VDP::Mathematics and natural science: 400::Mathematics: 410 | nb_NO |