Title of Document: QUANTUM MECHANICS AND QUANTUM INFORMATION THEORY Wesley William Van Camp, Doctor of Philosophy, 2009 Directed By: Distinguished University Professor and Chair of the Committee for Philosophy and the Sciences, Jeffrey Bub, Department of Philosophy The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretat...

If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. It is argued that virtually any deterministic nonlinear quantum theory will include such gates, and the method is explicitly demo...

We present a review of the current state of affairs in the foundations of quantum meachanics. After introducing the axioms of quantum theory, the first part of the report examines in detail the trials of interpreting quantum mechanics in a realist way. The main focus of the second half of the review is the attempt to describe quantum mechanics within a larger space of hypothetical theories. A p...

Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey this programme in terms of algebraic quantum theory.

Classical mechanics is formulated in Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of sem...

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing...

The methodology based on the association of the Variational Method with Supersymmetric Quantum Mechanics is used to evaluate the energy states of the confined hydrogen atom.

It is shown that the spanning set for L2([0, 1]) provided by the eigenfunctions {√2 sin(nπx)}∞ n=1 of the particle in a box in quantum mechanics provides a very effective variational basis for more general problems.The basis is scaled to [a, b], where a and b are then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box in Rd turns out ...

We demonstrate that reciprocal Maupertuis’ Principle is the classical limit of Schrödinger’s Variational Principle in Quantum Mechanics. Misha Marinov loved analytical mechanics and understood its beauty. Canonical transformations, Poisson structures, symplectic geometry etc. were the notions that he constantly used in his original papers, and in his famous review on path integral. One of the a...