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Author: N.B. Singh Publisher: N.B. Singh ISBN: Category : Science Languages : en Pages : 103
Book Description
"Number Theory in Quantum Mechanics" is a specialized exploration that bridges the realms of number theory and quantum mechanics. Catering to students, physicists, and researchers in quantum physics, this book investigates the intriguing connections between number theory concepts and quantum phenomena. Covering topics such as quantum states, operators, and wave functions, the book illuminates the mathematical underpinnings that emerge when applying number theory principles to quantum mechanics. With clarity and depth, this book serves as a valuable resource for those intrigued by the intersection of mathematical theory and quantum physics, offering new perspectives on the fundamental nature of quantum systems.
Author: N.B. Singh Publisher: N.B. Singh ISBN: Category : Science Languages : en Pages : 103
Book Description
"Number Theory in Quantum Mechanics" is a specialized exploration that bridges the realms of number theory and quantum mechanics. Catering to students, physicists, and researchers in quantum physics, this book investigates the intriguing connections between number theory concepts and quantum phenomena. Covering topics such as quantum states, operators, and wave functions, the book illuminates the mathematical underpinnings that emerge when applying number theory principles to quantum mechanics. With clarity and depth, this book serves as a valuable resource for those intrigued by the intersection of mathematical theory and quantum physics, offering new perspectives on the fundamental nature of quantum systems.
Author: Bartel L. van der Waerden Publisher: Springer Science & Business Media ISBN: 3642658601 Category : Mathematics Languages : en Pages : 220
Book Description
The German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". Its aim was, to explain the fundamental notions of the Theory of Groups and their Representations, and the application of this theory to the Quantum Mechanics of Atoms and Molecules. The book was mainly written for the benefit of physicists who were supposed to be familiar with Quantum Mechanics. However, it turned out that it was also used by. mathematicians who wanted to learn Quantum Mechanics from it. Naturally, the physical parts were too difficult for mathematicians, whereas the mathematical parts were sometimes too difficult for physicists. The German language created an additional difficulty for many readers. In order to make the book more readable for physicists and mathe maticians alike, I have rewritten the whole volume. The changes are most notable in Chapters 1 and 6. In Chapter t, I have tried to give a mathematically rigorous exposition of the principles of Quantum Mechanics. This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932. Chapter 6, on Molecule Spectra, was too much condensed in the German edition. I hope it is now easier to understand. In Chapter 2-5 too, numerous changes were made in order to make the book more readable and more useful.
Author: Jean-Marc Luck Publisher: Springer Science & Business Media ISBN: 3642754058 Category : Science Languages : en Pages : 324
Book Description
7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have involved more and more questions related to number theory, and in an increasingly direct way. This new trend is especially visible in two broad families of physical problems. The first class, dynamical systems and quasiperiodicity, includes classical and quantum chaos, the stability of orbits in dynamical systems, K.A.M. theory, and problems with "small denominators", as well as the study of incommensurate structures, aperiodic tilings, and quasicrystals. The second class, which includes the string theory of fundamental interactions, completely integrable models, and conformally invariant two-dimensional field theories, seems to involve modular forms and p adic numbers in a remarkable way.
Author: Sergio Albeverio Publisher: Springer Nature ISBN: 3030684903 Category : Mathematics Languages : en Pages : 316
Book Description
This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrödinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.
Author: Frederick W. Byron Publisher: Courier Corporation ISBN: 0486135063 Category : Science Languages : en Pages : 674
Book Description
Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.
Author: Valter Moretti Publisher: Springer ISBN: 331970706X Category : Mathematics Languages : en Pages : 950
Book Description
This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."
Author: N.B. Singh Publisher: N.B. Singh ISBN: Category : Mathematics Languages : en Pages : 89
Book Description
"A Handbook of Number Theory in Quantum Mechanics" is a comprehensive guide designed for absolute beginners eager to explore the fascinating intersection of number theory and quantum mechanics. This book provides a clear and accessible introduction to essential concepts in both fields, from prime numbers and modular arithmetic to wave functions and quantum superposition. With step-by-step explanations, illustrative examples, and a focus on clarity, it aims to make complex topics approachable for all readers. Whether you're a student, an enthusiastic amateur, or simply curious about the mathematical foundations of the quantum world, this handbook will equip you with a solid understanding and inspire further exploration into these captivating subjects.
Author: Manfred Schroeder Publisher: Springer Science & Business Media ISBN: 3540852972 Category : Science Languages : en Pages : 424
Book Description
"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudo primes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvelous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner
Author: Brian C. Hall Publisher: Springer Science & Business Media ISBN: 1461471168 Category : Science Languages : en Pages : 566
Book Description
Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.
Author: N.B. Singh
Author: N.B. Singh
Author: Bartel L. van der Waerden
Author: Jean-Marc Luck
Author: Sergio Albeverio
Author: Frederick W. Byron
Author: Valter Moretti
Author: N.B. Singh
Author: Manfred Schroeder
Author: Brian C. Hall
Author: George Whitelaw Mackey