Quantum Dynamics For Classical Systems

Author: Fabio Bagarello
Publisher: John Wiley & Sons
ISBN: 1118400607
Size: 52.66 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: 54.46 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: 64.70 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.

Introduction To Quantum Mechanics With Applications To Chemistry

Author: Linus Pauling
Publisher: Courier Corporation
ISBN: 0486134938
Size: 42.51 MB
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Classic undergraduate text explores wave functions for the hydrogen atom, perturbation theory, the Pauli exclusion principle, and the structure of simple and complex molecules. Numerous tables and figures.

Dynamical Systems Method And Applications

Author: Alexander G. Ramm
Publisher: John Wiley & Sons
ISBN: 111819960X
Size: 70.47 MB
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Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include: General nonlinear operator equations Operators satisfying a spectral assumption Newton-type methods without inversion of the derivative Numerical problems arising in applications Stable numerical differentiation Stable solution to ill-conditioned linear algebraic systems Throughout the chapters, the authors employ the use of figures and tables to help readers grasp and apply new concepts. Numerical examples offer original theoretical results based on the solution of practical problems involving ill-conditioned linear algebraic systems, and stable differentiation of noisy data. Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.

An Introduction To Theory And Applications Of Quantum Mechanics

Author: Amnon Yariv
Publisher: Courier Corporation
ISBN: 0486315878
Size: 68.72 MB
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Based on a Cal Tech introductory course for advanced undergraduates in applied physics, this text explores a wide range of topics culminating in semiconductor transistors and lasers. 1982 edition.

Quantum Mechanics With Applications To Nanotechnology And Information Science

Author: Yehuda B. Band
Publisher: Academic Press
ISBN: 0444537872
Size: 25.41 MB
Format: PDF, Kindle
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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 Methods In Quantum Mechanics

Author: Gerald Teschl
Publisher: American Mathematical Soc.
ISBN: 0821846604
Size: 38.20 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 Of Complex Molecular Systems

Author: David A. Micha
Publisher: Springer Science & Business Media
ISBN: 3540344608
Size: 50.84 MB
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Quantum phenomena are ubiquitous in complex molecular systems - as revealed by many experimental observations based upon ultrafast spectroscopic techniques - and yet remain a challenge for theoretical analysis. The present volume, based on a May 2005 workshop, examines and reviews the state-of-the-art in the development of new theoretical and computational methods to interpret the observed phenomena. Emphasis is on complex molecular processes involving surfaces, clusters, solute-solvent systems, materials, and biological systems. The research summarized in this book shows that much can be done to explain phenomena in systems excited by light or through atomic interactions. It demonstrates how to tackle the multidimensional dynamics arising from the atomic structure of a complex system, and addresses phenomena in condensed phases as well as phenomena at surfaces. The chapters on new methodological developments cover both phenomena in isolated systems, and phenomena which involve the statistical effects of an environment, such as fluctuations and dissipation. The methodology part explores new rigorous ways to formulate mixed quantum-classical dynamics in many dimensions, along with new ways to solve a many-atom Schroedinger equation, or the Liouville-von Neumann equation for the density operator, using trajectories and ideas related to hydrodynamics. Part I treats applications to complex molecular systems, and Part II covers new theoretical and computational methods

Quantum Dynamics

Author: Eric R. Bittner
Publisher: CRC
ISBN: 9781420080537
Size: 35.56 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 as they are poorly covered in standard texts. This text bridges the gap between what is traditionally taught in a one-semester quantum chemistry course and the modern field of chemical dynamics. It provides needed background in quantum mechanics and then discusses theory and a number of applications that are of current interest, from molecular electronics to photosynthesis. Written in a pedagogic style, it details needed computational components and sample calculations using Mathematica.