Cλ-extended oscillator algebras, where Cλ is the cyclic group of order λ, are introduced and realized as generalized deformed oscillator algebras. For λ = 2, they reduce to the well-known Calogero–Vasiliev algebra. For higher λ values, they are shown to provide in their bosonic Fock space representation some interesting applications to supersymmetric quantum mechanics and some variants thereof:...

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...

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...

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...

Non-relativistic quantum mechanics is necessarily an approximation to relativistic quantum mechanics. It is valid in the regime where kinetic energies and potential energies (more generally field energies) are much less than the rest mass energies of particles. Following philosophy of Laughlin (2005), I prefer to think of non-relativistic quantum mechanics as an emergent theory: one that is exa...