Hilbert Spaces Generalized Functions And Quantum Mechanics
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Hilbert Spaces Generalized Functions And Quantum Mechanics
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Author : Willi-Hans Steeb
language : en
Publisher:
Release Date : 1991
Hilbert Spaces Generalized Functions And Quantum Mechanics written by Willi-Hans Steeb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Hilbert space categories.
Trajectory Spaces Generalized Functions And Unbounded Operators
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Author : Stephanus van Eijndhoven
language : en
Publisher: Springer
Release Date : 2006-11-14
Trajectory Spaces Generalized Functions And Unbounded Operators written by Stephanus van Eijndhoven and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics
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Author : WILLI-HANS. MATHIS STEEB (WOLFGANG.)
language : en
Publisher: World Scientific Publishing Company
Release Date : 2022-09-24
Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics written by WILLI-HANS. MATHIS STEEB (WOLFGANG.) and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-24 with Mathematics categories.
This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.
Generalized Functions Operator Theory And Dynamical Systems
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Author : Ioannis Antoniou
language : en
Publisher: CRC Press
Release Date : 2021-02-25
Generalized Functions Operator Theory And Dynamical Systems written by Ioannis Antoniou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-25 with Mathematics categories.
Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume." This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods.
General Principles Of Quantum Field Theory
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Author : N.N. Bogolubov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
General Principles Of Quantum Field Theory written by N.N. Bogolubov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The majority of the "memorable" results of relativistic quantum theory were obtained within the framework of the local quantum field approach. The explanation of the basic principles of the local theory and its mathematical structure has left its mark on all modern activity in this area. Originally, the axiomatic approach arose from attempts to give a mathematical meaning to the quantum field theory of strong interactions (of Yukawa type). The fields in such a theory are realized by operators in Hilbert space with a positive Poincare-invariant scalar product. This "classical" part of the axiomatic approach attained its modern form as far back as the sixties. * It has retained its importance even to this day, in spite of the fact that nowadays the main prospects for the description of the electro-weak and strong interactions are in connection with the theory of gauge fields. In fact, from the point of view of the quark model, the theory of strong interactions of Wightman type was obtained by restricting attention to just the "physical" local operators (such as hadronic fields consisting of ''fundamental'' quark fields) acting in a Hilbert space of physical states. In principle, there are enough such "physical" fields for a description of hadronic physics, although this means that one must reject the traditional local Lagrangian formalism. (The connection is restored in the approximation of low-energy "phe nomenological" Lagrangians.
Hilbert Spaces Wavelets Generalised Functions And Modern Quantum Mechanics
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Author : W.-H. Steeb
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-30
Hilbert Spaces Wavelets Generalised Functions And Modern Quantum Mechanics written by W.-H. Steeb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-30 with Science categories.
This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. The book is suitable for graduate students in physics and mathematics.
Generalized Functions Volume 3
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Author : I. M. Gel'fand
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-30
Generalized Functions Volume 3 written by I. M. Gel'fand and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with Mathematics categories.
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel'fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. In Volume 3, applications of generalized functions to the Cauchy problem for systems of partial differential equations with constant coefficients are considered. The book includes the study of uniqueness classes of solutions of the Cauchy problem and the study of classes of functions where the Cauchy problem is well posed. The last chapter of this volume presents results related to spectral decomposition of differential operators related to generalized eigenfunctions.
Elementary Introduction To New Generalized Functions
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Author : J.F. Colombeau
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Elementary Introduction To New Generalized Functions written by J.F. Colombeau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
The author's previous book `New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introduced `new generalized functions' in order to explain heuristic computations of Physics and to give a meaning to any finite product of distributions. The aim here is to present these functions in a more direct and elementary way. In Part I, the reader is assumed to be familiar only with the concepts of open and compact subsets of R&eegr;, of C∞ functions of several real variables and with some rudiments of integration theory. Part II defines tempered generalized functions, i.e. generalized functions which are, in some sense, increasing at infinity no faster than a polynomial (as well as all their partial derivatives). Part III shows that, in this setting, the partial differential equations have new solutions. The results obtained show that this setting is perfectly adapted to the study of nonlinear partial differential equations, and indicate some new perspectives in this field.
Quantum Mechanics Using Computer Algebra
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Author : Willi-hans Steeb
language : en
Publisher: World Scientific Publishing Company
Release Date : 1994-05-23
Quantum Mechanics Using Computer Algebra written by Willi-hans Steeb and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-23 with Science categories.
Solving problems in quantum mechanics is an essential skill and research activity for scientists, engineers and others. Nowadays the labor of scientific computation has been greatly eased by the advent of computer algebra packages. These do not merely perform number-crunching tasks, but enable users to manipulate algebraic expressions and equations symbolically. For example, differentiation and integration can now be carried out algebraically by the computer.This book collects standard and advanced methods in quantum mechanics and implements them using REDUCE, a popular computer algebra package. Throughout, sample programs and their output have been displayed alongside explanatory text, making the book easy to follow. Selected problems have also been implemented using two other popular packages, MATHEMATICA and MAPLE, and in the object-oriented programming language C++.Besides standard quantum mechanical techniques, modern developments in quantum theory are also covered. These include Fermi and Bose Operators, coherent states, gauge theory and quantum groups. All the special functions relevant to quantum mechanics (Hermite, Chebyshev, Legendre and more) are implemented.The level of presentation is such that one can get a sound grasp of computational techniques early on in one's scientific education. A careful balance is struck between practical computation and the underlying mathematical concepts, making the book well-suited for use with quantum mechanics courses.
Lectures On Quantum Mechanics
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Author : Philip L. Bowers
language : en
Publisher: Cambridge University Press
Release Date : 2020-09-17
Lectures On Quantum Mechanics written by Philip L. Bowers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-17 with Science categories.
Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.