Essential Quantum Calculus
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Essential Quantum Calculus
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
Essential Quantum Calculus written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
"Essential Quantum Calculus" is a concise and accessible guide that demystifies quantum calculus, offering readers a fundamental understanding of its principles. This book provides a clear introduction to the mathematical concepts essential for grasping quantum mechanics, making it an indispensable resource for students and enthusiasts seeking a solid foundation in the intricate world of quantum physics
Quantum Calculus
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Author : Victor Kac
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Calculus written by Victor Kac 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 Mathematics categories.
Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by MIT Professor Kac over the last few years at MIT.
Quantum Measure Theory
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Author : J. Hamhalter
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Quantum Measure Theory written by J. Hamhalter 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 2013-03-14 with Mathematics categories.
This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.
Logic And Probability In Quantum Mechanics
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Author : Patrick Suppes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Logic And Probability In Quantum Mechanics written by Patrick Suppes 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 2013-11-11 with Science categories.
During the academic years 1972-1973 and 1973-1974, an intensive sem inar on the foundations of quantum mechanics met at Stanford on a regular basis. The extensive exploration of ideas in the seminar led to the org~ization of a double issue of Synthese concerned with the foundations of quantum mechanics, especially with the role of logic and probability in quantum meChanics. About half of the articles in the volume grew out of this seminar. The remaining articles have been so licited explicitly from individuals who are actively working in the foun dations of quantum mechanics. Seventeen of the twenty-one articles appeared in Volume 29 of Syn these. Four additional articles and a bibliography on -the history and philosophy of quantum mechanics have been added to the present volume. In particular, the articles by Bub, Demopoulos, and Lande, as well as the second article by Zanotti and myself, appear for the first time in the present volume. In preparing the articles for publication I am much indebted to Mrs. Lillian O'Toole, Mrs. Dianne Kanerva, and Mrs. Marguerite Shaw, for their extensive assistance.
Quantum Mechanics A Half Century Later
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Author : J.L. Lopes
language : en
Publisher: Springer Science & Business Media
Release Date : 1977-09-30
Quantum Mechanics A Half Century Later written by J.L. Lopes 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 1977-09-30 with Science categories.
The articles collected in this volume were written for a Colloquium on Fifty Years of Quantum Mechanics which was held at the University Louis Pasteur of Strasbourg on May 2-4, 1974, in commemoration of the original work by De Broglie in 1924. It is our hope that this volume will convey to the reader the idea that quantum mechanics, besides being a fundamental tool for scien tific workers today, is also a source of a number of questions and thoughts about the interpretation of the foundation of quantum mechanics itself. This gives rise to problems of a philosophical and logical character and has repercussions on other domains such as the theory of gravitation. Besides the papers presented at the Colloquium, an article has been included by D. Bohm and B. Hiley. This compensates, perhaps, for the article of S. Kochen, whose manuscript unfortunately did not reach us in time for inclusion in ~his volume. A few months after this Colloquium we learned of the death of Professor Jauch, who had taken a lively and crucial part in its discussions. We have been extremely saddened by the news of his death, and would like to express our long standing indebtedness to him as a physicist.
Unifying Themes In Complex Systems Volume 1
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Author : Yaneer Bar-yam
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Unifying Themes In Complex Systems Volume 1 written by Yaneer Bar-yam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
The study of complex systems has attracted a broad range of researchers from many disciplines spanning both the hard and soft sciences. In the Autumn of 1997, 300 of these researchers came together for the First International Conference on Complex Systems. The proceedings of this conference is the first book in the New England Complex Systems Institute Series on Complexity and includes more than 100 presentations and papers on topics like evolution, emergence, complexity, self-organization, scaling, informatics, time series, emergence of mind, and engineering of complex systems.
Basic Modern Theory Of Linear Complex Analytic Q Difference Equations
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Author : Jacques Sauloy
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-06
Basic Modern Theory Of Linear Complex Analytic Q Difference Equations written by Jacques Sauloy and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.
The roots of the modern theories of differential and $q$-difference equations go back in part to an article by George D. Birkhoff, published in 1913, dealing with the three ?sister theories? of differential, difference and $q$-difference equations. This book is about $q$-difference equations and focuses on techniques inspired by differential equations, in line with Birkhoff's work, as revived over the last three decades. It follows the approach of the Ramis school, mixing algebraic and analytic methods. While it uses some $q$-calculus and is illustrated by $q$-special functions, these are not its main subjects. After a gentle historical introduction with emphasis on mathematics and a thorough study of basic problems such as elementary $q$-functions, elementary $q$-calculus, and low order equations, a detailed algebraic and analytic study of scalar equations is followed by the usual process of transforming them into systems and back again. The structural algebraic and analytic properties of systems are then described using $q$-difference modules (Newton polygon, filtration by the slopes). The final chapters deal with Fuchsian and irregular equations and systems, including their resolution, classification, Riemann-Hilbert correspondence, and Galois theory. Nine appendices complete the book and aim to help the reader by providing some fundamental yet not universally taught facts. There are 535 exercises of various styles and levels of difficulty. The main prerequisites are general algebra and analysis as taught in the first three years of university. The book will be of interest to expert and non-expert researchers as well as graduate students in mathematics and physics.
Difference Equations Discrete Dynamical Systems And Applications
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Author : Martin Bohner
language : en
Publisher: Springer
Release Date : 2015-12-01
Difference Equations Discrete Dynamical Systems And Applications written by Martin Bohner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-01 with Mathematics categories.
These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference Equations (ISDE) in July 2014. Its purpose was to bring together renowned researchers working actively in the respective fields, to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book will appeal to researchers and scientists working in the fields of difference equations, discrete dynamical systems and their applications.
Discrete Fractional Calculus
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Author : Christopher Goodrich
language : en
Publisher: Springer
Release Date : 2016-02-09
Discrete Fractional Calculus written by Christopher Goodrich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-09 with Mathematics categories.
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject. Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1—2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1—2 may be covered quickly and readers may then skip to Chapters 6—7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6—7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1—5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.
Quantum Variational Calculus
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Author : Agnieszka B. Malinowska
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-29
Quantum Variational Calculus written by Agnieszka B. Malinowska 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 2013-11-29 with Mathematics categories.
This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.