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Quantum Dynamics For Classical Systems

Author: Fabio Bagarello
Publisher: John Wiley & Sons
ISBN: 1118400607
Size: 72.84 MB
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Introduces number operators with a focus on the relationship between quantum mechanics and social science Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models Illustrations of the use of creation and annihilation operators for classical problems Examples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics Clarification on numerous misunderstandings and misnomers while shedding light on new approaches in the field Quantum Dynamics for Classical Systems is an ideal reference for researchers, professionals, and academics in applied mathematics, economics, physics, biology, and sociology. The book is also excellent for courses in dynamical systems, quantum mechanics, and mathematical models.

Non Selfadjoint Operators In Quantum Physics

Author: Fabio Bagarello
Publisher: John Wiley & Sons
ISBN: 1118855272
Size: 43.78 MB
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A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.

Operator Methods In Quantum Mechanics

Author: Martin Schechter
Publisher: Courier Corporation
ISBN: 0486150046
Size: 66.50 MB
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This text introduces techniques related to physical theory. Entire book is devoted to a particle moving in a straight line; students develop techniques by answering questions about the particle. 1981 edition.

Mathematical Methods In Quantum Mechanics

Author: Gerald Teschl
Publisher: American Mathematical Soc.
ISBN: 0821846604
Size: 36.17 MB
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Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).

Quantum Dynamics

Author: Eric R. Bittner
Publisher: CRC Press
ISBN: 1439882142
Size: 66.61 MB
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Even though time-dependent spectroscopic techniques continue to push the frontier of chemical physics, they receive scant mention in introductory courses and are poorly covered in standard texts. Quantum Dynamics: Applications in Biological and Materials Systems bridges the gap between what is traditionally taught in a one-semester quantum chemistry course and the modern field of chemical dynamics, presenting the quantum theory of charge and energy transport in biological systems and optical-electronic materials from a dynamic perspective. Reviews the basics Taking a pedagogical approach, the book begins by reviewing the concepts of classical mechanics that are necessary for studying quantum mechanics. It discusses waves and wave functions and then moves on to an exploration of semiclassical quantum mechanics methods, an important part of the development and utilization of quantum theory. Time-independent and time-dependent perspectives The main focus of the book is the chapter on quantum dynamics, which begins with a brief review of the bound states of a coupled two-level system. This is discussed with a time-independent as well as a time-dependent perspective. The book also explores what happens when the two-level system has an additional harmonic degree of freedom that couples the transitions between the two states. The book reviews different ways in which one can represent the evolution of a quantum state, explores the quantum density matrix, and examines the basis for excitation energy transfer between molecules. Later chapters describe the pi electronic structure of conjugated organic systems and discuss electron-phonon coupling in conjugated systems and transport and dynamics in extended systems. Includes Mathematica® downloads On an accompanying website, Mathematica® applications and codes can be downloaded to illustrate the theoretical methods presented, and the book offers ample references for further study. The book and website combine to provide students with a clear understanding of the theory and its applications.

Quantum Mechanics With Applications To Nanotechnology And Information Science

Author: Yehuda B. Band
Publisher: Academic Press
ISBN: 0444537872
Size: 76.85 MB
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Quantum mechanics transcends and supplants classical mechanics at the atomic and subatomic levels. It provides the underlying framework for many subfields of physics, chemistry and materials science, including condensed matter physics, atomic physics, molecular physics, quantum chemistry, particle physics, and nuclear physics. It is the only way we can understand the structure of materials, from the semiconductors in our computers to the metal in our automobiles. It is also the scaffolding supporting much of nanoscience and nanotechnology. The purpose of this book is to present the fundamentals of quantum theory within a modern perspective, with emphasis on applications to nanoscience and nanotechnology, and information-technology. As the frontiers of science have advanced, the sort of curriculum adequate for students in the sciences and engineering twenty years ago is no longer satisfactory today. Hence, the emphasis on new topics that are not included in older reference texts, such as quantum information theory, decoherence and dissipation, and on applications to nanotechnology, including quantum dots, wires and wells. This book provides a novel approach to Quantum Mechanics whilst also giving readers the requisite background and training for the scientists and engineers of the 21st Century who need to come to grips with quantum phenomena The fundamentals of quantum theory are provided within a modern perspective, with emphasis on applications to nanoscience and nanotechnology, and information-technology Older books on quantum mechanics do not contain the amalgam of ideas, concepts and tools necessary to prepare engineers and scientists to deal with the new facets of quantum mechanics and their application to quantum information science and nanotechnology As the frontiers of science have advanced, the sort of curriculum adequate for students in the sciences and engineering twenty years ago is no longer satisfactory today There are many excellent quantum mechanics books available, but none have the emphasis on nanotechnology and quantum information science that this book has

Mathematical Concepts Of Quantum Mechanics

Author: Stephen J. Gustafson
Publisher: Springer Science & Business Media
ISBN: 3642218660
Size: 62.47 MB
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The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.

Mathematical Foundations Of Quantum Information And Computation And Its Applications To Nano And Bio Systems

Author: Masanori Ohya
Publisher: Springer Science & Business Media
ISBN: 9789400701717
Size: 60.23 MB
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This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.