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A Mathematical Primer on Quantum Mechanics
This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.
Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
Advances In Dynamical Systems And Quantum Physics - Proceedings Of The Conference
This volume contains contributions from the meeting held in honour of G.F. Dell'Antonio for his sixtieth birthday. The topics covered include the theory of classical and quantum dynamical systems and related mathematical disciplines such as functional and stochastic analysis, operator algebras etc. The contributions by leading specialists survey recent developments in Hamiltonian dynamics, non-commutative integration, supersymmetric theories, spin glass theory and other subjects in mathematical physics.
Quantum Dynamics of a Particle in a Tracking Chamber
In the original formulation of quantum mechanics the existence of a precise border between a microscopic world, governed by quantum mechanics, and a macroscopic world, described by classical mechanics was assumed. Modern theoretical and experimental physics has moved that border several times, carefully investigating its definition and making available to observation larger and larger quantum systems. The present book examines a paradigmatic case of the transition from quantum to classical behavior: A quantum particle is revealed in a tracking chamber as a trajectory obeying the laws of classical mechanics. The authors provide here a purely quantum-mechanical description of this behavior, thus helping to illuminate the nature of the border between the quantum and the classical.
Direction of Time
This edited book presents the problems of time and direction from an interdisciplinary point of view, concentrating in particular on the following relations: • Time and physics • Time, philosophy and psychology • Time, mathematics and information theory It is a unique contribution by philosophers and scientists who are active in mathematics, physics, biology, engineering, information theory and psychology. Questions such as the existence of a Big Bang, the neurobiological basis regarding the coexistence of free will and determinism, intercultural aspects of time, mathematical models of time, psychopathological features of time, and micro reversibility versus macroscopic irreversibility are studied. It also provides a truly interdisciplinary study of the problematic 'arrow of time'.
Inverse Problems and Imaging
Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics.
Quantum and Stochastic Mathematical Physics
Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of the Random Transformations and Invariance in Stochastic Dynamics Workshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of (non Gaussian)-SPDEs, the related theory of (pseudo-)differential operators, and ergodic theory had...
Geometry and Invariance in Stochastic Dynamics
This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of ...
Operator Theory, Analysis and Mathematical Physics
This volume contains lectures delivered at the International Conference Operator Theory and its Applications in Mathematical Physics (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics.
Determinism, Holism, and Complexity
Determinism, holism and complexity: three epistemological attitudes that have easily identifiable historical origins and developments. Galileo believed that it was necessary to "prune the impediments" to extract the mathematical essence of physical phenomena, to identify the math ematical structures representing the underlying laws. This Galilean method was the key element in the development of Physics, with its extraordinary successes. Nevertheless the method was later criticized because it led to a view of nature as essentially "simple and orderly", and thus by choosing not to investigate several charac teristics considered as an "impediment", several essential aspects of the phenomenon un...
