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Finite Approximations of Quantum Systems in a Non-Archimedean and Archimedean Setting

Bakken, Erik Makino
Doctoral thesis
Åpne
Fulltext (PDF) available (Låst)
Permanent lenke
http://hdl.handle.net/11250/2399941
Utgivelsesdato
2016
Metadata
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Samlinger
  • Institutt for matematiske fag [1793]
Sammendrag
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.
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NTNU
Serie
Doctoral thesis at NTNU;2016:212

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