LECTURES ON QUANTUM MECHANICS AND ATTRACTORS

類似書籍推薦給您

This book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations. The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices. The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study. Sample Chapter(s) Preface Introduction Section I.1-I.4 Contents: Preface Introduction Nonrelativistic Quantum Mechanics Scattering of Light and Particles Atom in Magnetic Field Relativistic Quantum Mechanics Quantum Postulates and Attractors Attractors of Hamiltonian PDEs Appendices: Old Quantum Theory The Noether Theory of Invariants Perturbation Theory Bibliography Index Readership: Discipline/profession: Physics and Mathematics. Sector: university, academia and industry. Level: Graduate students and advanced undergraduate students physicists, chemists and mathematicians, lecturers in Quantum Mechanics.

An Introduction to Nonautonomous Dynamical Systems and their Attractors

類似書籍推薦給您

The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required. In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other. The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant. Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a "Thousand Expert" Professorship at the Huazhong University of Science and Technology in Wuhan.