Algebraic modelling of quantum mechanical equations in the finite- and infinite-dimensional Hilbert spaces

Dwight Megill, Norman (2011) Algebraic modelling of quantum mechanical equations in the finite- and infinite-dimensional Hilbert spaces. Doctoral thesis, Faculty of Science > Department of Physics.

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Abstract

The Hilbert space of quantum mechanics has a dual representation in lattice theory, called the Hilbert lattice. In addition to offering the potential for new insights, the lattice-theoretical approach may be computationally efficient for certain kinds of quantum mechanics problems, particularly if, in the future, we are able to exploit what may be a “natural” fit with quantum computation. The equations that hold in the Hilbert space lattice representation are not completely known and are poorly understood, although much progress has been made in the last several years. This work contributes to the development of these equations, with special attention to the so-called generalized orthoarguesian equations. Many new results that do not appear in the literature are given, along with their detailed proofs. In addition, possible approaches for work towards answering some remaining open questions are discussed.

Item Type: Thesis (Doctoral thesis)
Keywords: Hilbert space ; Hilbert lattice ; orthoarguesian property ; strong state ; quantum logic ; quantum computation ; Godowski equations ; orthomodular lattice
Supervisor: Pavičić, Mladen
Date: 14 December 2011
Number of Pages: 183
Subjects: NATURAL SCIENCES > Physics
Divisions: Faculty of Science > Department of Physics
Depositing User: Gordana Stubičan Ladešić
Date Deposited: 21 Dec 2013 23:27
Last Modified: 21 Dec 2013 23:28
URI: http://digre.pmf.unizg.hr/id/eprint/42

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