Asymptotic Methods In Quantum Mechanics

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Asymptotic Methods in Quantum Mechanics

Author : S.H. Patil
Publisher : Springer Science & Business Media
ISBN 13 : 3642573177
Total Pages : 178 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Asymptotic Methods in Quantum Mechanics by : S.H. Patil

Download or read book Asymptotic Methods in Quantum Mechanics written by S.H. Patil and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here.

Asymptotic Methods in Quantum Mechanics

Author : S H Patil
Publisher :
ISBN 13 : 9783642573187
Total Pages : 194 pages
Book Rating : 4.5/5 (731 download)

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Book Synopsis Asymptotic Methods in Quantum Mechanics by : S H Patil

Download or read book Asymptotic Methods in Quantum Mechanics written by S H Patil and published by . This book was released on 2000-04-26 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes some general properties of wave functions, with an emphasis on their asymptotic behaviour. The asymptotic region is particularly important since it is the wave function in the outer region of an atom, a molecule or a nucleus, which is sensitive to external interaction. An analysis of these properties helps in constructing simple and compact wave functions and in developing a broad understanding of different aspects of the quantum mechanics of many-particle systems. As applications, wave functions with correct asymptotic forms are used to generate a large data base for susceptibilities, polarizabilities, interatomic potentials, and nuclear densities.

Asymptotic Methods for Wave and Quantum Problems

Author : M. V. Karasev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821833360
Total Pages : 298 pages
Book Rating : 4.8/5 (333 download)

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Book Synopsis Asymptotic Methods for Wave and Quantum Problems by : M. V. Karasev

Download or read book Asymptotic Methods for Wave and Quantum Problems written by M. V. Karasev and published by American Mathematical Soc.. This book was released on 2003 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.

Asymptotic Theory of Quantum Statistical Inference

Author : Masahito Hayashi
Publisher : World Scientific
ISBN 13 : 981448198X
Total Pages : 560 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Asymptotic Theory of Quantum Statistical Inference by : Masahito Hayashi

Download or read book Asymptotic Theory of Quantum Statistical Inference written by Masahito Hayashi and published by World Scientific. This book was released on 2005-02-21 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s). This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now. The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference. Contents:Hypothesis TestingQuantum Cramér-Rao Bound in Mixed States ModelQuantum Cramér-Rao Bound in Pure States ModelGroup Symmetric Approach to Pure States ModelLarge Deviation Theory in Quantum EstimationFuther Topics on Quantum Statistical Inference Readership: Graduate students in quantum physics, mathematical physics, and probability and statistics. Keywords:Quantum Information;Estimation Theory;Statistics;Statistical Inference;Mathematical Physics;Asymptotic Theory;Hypothesis TestingReviews:“This book will give the scholars new insight into physics and statistical inference.”Zentralblatt MATH '

Semi-Classical Approximation in Quantum Mechanics

Author : Victor P. Maslov
Publisher : Springer Science & Business Media
ISBN 13 : 9781402003066
Total Pages : 320 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Semi-Classical Approximation in Quantum Mechanics by : Victor P. Maslov

Download or read book Semi-Classical Approximation in Quantum Mechanics written by Victor P. Maslov and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. The book is, in fact, an extension and continuation of the authors' works [59], [60], [65]. The basic ideas are summarized in the Introduction. The book consists of two parts. In the first, the theory of the canonical operator is develop ed, whereas, in the second, many applications of the canonical operator method to concrete problems of mathematical physics are presented. The authors are pleased to express their deep gratitude to S. M. Tsidilin for his valuable comments. THE AUTHORS IX INTRODUCTION 1. Various problems of mathematical and theoretical physics involve partial differential equations with a small parameter at the highest derivative terms. For constructing approximate solutions of these equations, asymptotic methods have long been used. In recent decades there has been a renaissance period of the asymptotic methods of linear mathematical physics. The range of their applicability has expanded: the asymptotic methods have been not only continuously used in traditional branches of mathematical physics but also have had an essential impact on the development of the general theory of partial differential equations. It appeared recently that there is a unified approach to a number of problems which, at first sight, looked rather unrelated.

Asymptotic Time Decay in Quantum Physics

Author : Domingos H. U. Marchetti
Publisher : World Scientific
ISBN 13 : 9814383805
Total Pages : 362 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Asymptotic Time Decay in Quantum Physics by : Domingos H. U. Marchetti

Download or read book Asymptotic Time Decay in Quantum Physics written by Domingos H. U. Marchetti and published by World Scientific. This book was released on 2013 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time decays form the basis of a multitude of important and interesting phenomena in quantum physics that range from spectral properties, resonances, return and approach to equilibrium, to quantum mixing, dynamical stability preperties and irreversibility and the "arrow of time." This monograph is devoted to a clear and precise, yet pedagogical account of the associated concepts and methods.

Mathematical Methods in Quantum Mechanics

Author : Gerald Teschl
Publisher : American Mathematical Soc.
ISBN 13 : 0821846604
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mathematical Methods in Quantum Mechanics by : Gerald Teschl

Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2009 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Asymptotic Methods for Wave and Quantum Problems

Author : Mikhail Vladimirovich Karasev
Publisher :
ISBN 13 : 9781470434199
Total Pages : 284 pages
Book Rating : 4.4/5 (341 download)

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Book Synopsis Asymptotic Methods for Wave and Quantum Problems by : Mikhail Vladimirovich Karasev

Download or read book Asymptotic Methods for Wave and Quantum Problems written by Mikhail Vladimirovich Karasev and published by . This book was released on 2003 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper "Quantization and Intrinsic Dynamics" a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approxi.

Approximation Methods in Quantum Mechanics

Author : Arkadiĭ Beĭnusovich Migdal
Publisher :
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Approximation Methods in Quantum Mechanics by : Arkadiĭ Beĭnusovich Migdal

Download or read book Approximation Methods in Quantum Mechanics written by Arkadiĭ Beĭnusovich Migdal and published by . This book was released on 1969 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dimensional and "model" approximations -- Various types of perturbation theory -- The quasiclassical approximation.

Multiscale Methods in Quantum Mechanics

Author : Philippe Blanchard
Publisher : Springer Science & Business Media
ISBN 13 : 0817682023
Total Pages : 223 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Multiscale Methods in Quantum Mechanics by : Philippe Blanchard

Download or read book Multiscale Methods in Quantum Mechanics written by Philippe Blanchard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics.

Short-Wavelength Diffraction Theory

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Author : Vasili M. Babic
Publisher : Springer
ISBN 13 : 9783642834615
Total Pages : 0 pages
Book Rating : 4.8/5 (346 download)

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Book Synopsis Short-Wavelength Diffraction Theory by : Vasili M. Babic

Download or read book Short-Wavelength Diffraction Theory written by Vasili M. Babic and published by Springer. This book was released on 2011-12-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.

Scattering Theory of Classical and Quantum N-Particle Systems

Author : Jan Derezinski
Publisher : Springer Science & Business Media
ISBN 13 : 3662034034
Total Pages : 448 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Scattering Theory of Classical and Quantum N-Particle Systems by : Jan Derezinski

Download or read book Scattering Theory of Classical and Quantum N-Particle Systems written by Jan Derezinski and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses researchers and students. It is a modern presentation of time-dependent methods for studying problems of scattering theory in the classical and quantum mechanics of N-particle systems. Particular attention is paid to long-range potentials. For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding. As a special feature of the book, the beautiful analogy between classical and quantum scattering theory (e.g., for N-body Hamiltonians) is presented with deep insight into the physical and mathematical problems.

Qualitative Methods In Quantum Theory

Author : Migdal
Publisher : CRC Press
ISBN 13 : 0429977573
Total Pages : 141 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Qualitative Methods In Quantum Theory by : Migdal

Download or read book Qualitative Methods In Quantum Theory written by Migdal and published by CRC Press. This book was released on 2018-03-05 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book, written by a leading Soviet theorist, is not a textbook of quantum mechanics but rather a compendium of the "tricks of the trade"-the methods that all practicing theoretical physicists use but few have set down in writing.

Quantum Mechanics I

Author : S. Rajasekar
Publisher : CRC Press
ISBN 13 : 100072901X
Total Pages : 606 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Quantum Mechanics I by : S. Rajasekar

Download or read book Quantum Mechanics I written by S. Rajasekar and published by CRC Press. This book was released on 2022-11-28 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems. This fully updated new edition addresses many topics not typically found in books at this level, including: Bound state solutions of quantum pendulum Morse oscillator Solutions of classical counterpart of quantum mechanical systems A criterion for bound state Scattering from a locally periodic potential and reflection-less potential Modified Heisenberg relation Wave packet revival and its dynamics An asymptotic method for slowly varying potentials Klein paradox, Einstein-Podolsky-Rosen (EPR) paradox, and Bell’s theorem Delayed-choice experiments Fractional quantum mechanics Numerical methods for quantum systems A collection of problems at the end of each chapter develops students’ understanding of both basic concepts and the application of theory to various physically important systems. This book, along with the authors’ follow-up Quantum Mechanics II: Advanced Topics, provides students with a broad, up-to-date introduction to quantum mechanics. Print Versions of this book also include access to the ebook version.

Statistical Structure of Quantum Theory

Author : Alexander S. Holevo
Publisher : Springer Science & Business Media
ISBN 13 : 3540449981
Total Pages : 166 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Statistical Structure of Quantum Theory by : Alexander S. Holevo

Download or read book Statistical Structure of Quantum Theory written by Alexander S. Holevo and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.

Quantum Theory

Author : D. R. Bates
Publisher : Academic Press
ISBN 13 : 1483275884
Total Pages : 466 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Quantum Theory by : D. R. Bates

Download or read book Quantum Theory written by D. R. Bates and published by Academic Press. This book was released on 2013-10-22 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postulates, and time-dependent states. The text then examines the stationary perturbation theory, variational method, and the asymptotic approximation method. Concerns cover the application of the asymptotic approximation method to potential barrier problems, method of linear combinations, lower bounds for the ground state eigenenergy, relative degeneracy, and degenerate case. The publication examines the theory of collisions and transitions, including the scattering of identical particles, Coulomb field, methods of determining scattering phases, persistent perturbations, and adiabatic approximation. The selection is a valuable source of information for researchers interested in quantum theory.

Asymptotic Methods for Engineers

Author : Igor V. Andrianov
Publisher : CRC Press
ISBN 13 : 1040032710
Total Pages : 265 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Asymptotic Methods for Engineers by : Igor V. Andrianov

Download or read book Asymptotic Methods for Engineers written by Igor V. Andrianov and published by CRC Press. This book was released on 2024-05-16 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).