This digital library contains scholarly publications by Thomas Arthur Osborn and collaborators, spanning research in quantum mechanics, scattering theory, phase space methods, and mathematical physics. Each publication includes metadata in multiple linked data formats for interoperability.
2010s
New Proposition 1
Development of a new proposition regarding quantum bounds and their relationship to Bell inequalities. The paper presents mathematical results concerning the structure of quantum mechanical violations...
Proposition 1 with dim H
Extension of Proposition 1 incorporating Hilbert space dimension considerations. The paper analyzes how quantum bounds depend on the dimension of the underlying Hilbert space and derives dimension-dep...
On the Maximum Quantum Gap
Analysis of the maximum quantum gap in the context of Bell inequalities and quantum bounds. The paper investigates the conditions under which quantum mechanics achieves its maximum violation of classi...
HV-Quantum Gap Properties
Research notes on HV-quantum gap properties, examining unique features associated with Bell matrices. The B(N) Bell matrix HV-quantum gap is analyzed with explicit formulas for the gap function G_X(N)...
2000s
Cotangent Bundle Quantization: Entangling of Metric and Magnetic Field
The quantization of systems on cotangent bundles is studied, revealing the entanglement between metric and magnetic field structures. The analysis shows how the geometry of configuration space and the...
Quantum Magnetic Algebra and Magnetic Curvature
A quantum magnetic algebra is developed that incorporates the effects of magnetic curvature on the dynamics of charged particles. The formalism extends the standard treatment of particles in magnetic ...
On the Notion of Quantum Lyapunov Exponent
Classical chaos refers to the property of trajectories to diverge exponentially as time t → ∞. It is characterized by a positive Lyapunov exponent. The purpose of this note is to show how the definiti...
Symplectic Areas, Quantization and Dynamics in Electromagnetic Fields
The role of symplectic area quantization in the dynamics of charged particles in electromagnetic fields is investigated. The connection between symplectic geometry and quantum mechanics is explored th...
1990s
Heisenberg Evolution WKB and Symplectic Area Phases
The semiclassical approximation for Heisenberg time evolution is developed with emphasis on the role of symplectic area phases. The WKB expansion is shown to be intimately connected to the geometry of...
Mixed Weyl Symbol Calculus and Spectral Line Shape Theory
A mixed Weyl symbol calculus is developed and applied to spectral line shape theory. The formalism combines aspects of the Weyl-Wigner representation with techniques suitable for analyzing spectral pr...
Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics
The Moyal formalism of quantum mechanics is developed to study the semiclassical Heisenberg dynamics. The phase space formulation of quantum mechanics provides a natural framework for analyzing the cl...
A Phase-space Technique for the Perturbation Expansion of Schrödinger Propagators
We develop a perturbation theory for Schrödinger and heat equations that is based on phase space variables. The Dyson series representing the evolution kernel is described in terms of two basic classi...
The Wigner-Weyl Transform on Tori and Connected Graph Propagator Representations
For a quantum system set on the manifold T^e × R^d, a connected graph expansion is obtained for the Schrödinger propagator with scalar interactions. A definition of the Wigner transform suitable for t...
1970s
An S-Matrix Approach to Glauber Theory
We present an S-matrix approach to Glauber theory based on an eikonal-Hamiltonian formalism. The variant of Glauber's multiple diffraction theory obtained here is rigorously unitary. The construction ...
The Three-Body Problem
This thesis presents a comprehensive study of the quantum mechanical three-body problem.