Number Theory In Quantum Mechanics

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Group Theory and Quantum Mechanics

Author : Bartel L. van der Waerden
Publisher : Springer Science & Business Media
ISBN 13 : 3642658601
Total Pages : 220 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Group Theory and Quantum Mechanics by : Bartel L. van der Waerden

Download or read book Group Theory and Quantum Mechanics written by Bartel L. van der Waerden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Number Theory in Quantum Mechanics

Author : N.B. Singh
Publisher : N.B. Singh
ISBN 13 :
Total Pages : 103 pages
Book Rating : 4./5 ( download)

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Book Synopsis Number Theory in Quantum Mechanics by : N.B. Singh

Download or read book Number Theory in Quantum Mechanics written by N.B. Singh and published by N.B. Singh. This book was released on with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Number Theory and Physics

Author : Jean-Marc Luck
Publisher : Springer Science & Business Media
ISBN 13 : 3642754058
Total Pages : 324 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Number Theory and Physics by : Jean-Marc Luck

Download or read book Number Theory and Physics written by Jean-Marc Luck and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory in Quantum Mechanics

Author : Volker Heine
Publisher : Elsevier
ISBN 13 : 1483152006
Total Pages : 479 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Group Theory in Quantum Mechanics by : Volker Heine

Download or read book Group Theory in Quantum Mechanics written by Volker Heine and published by Elsevier. This book was released on 2014-05-15 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Theory in Quantum Mechanics: An Introduction to its Present Usage introduces the reader to the three main uses of group theory in quantum mechanics: to label energy levels and the corresponding eigenstates; to discuss qualitatively the splitting of energy levels as one starts from an approximate Hamiltonian and adds correction terms; and to aid in the evaluation of matrix elements of all kinds, and in particular to provide general selection rules for the non-zero ones. The theme is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave functions. This book is comprised of eight chapters and begins with an overview of the necessary mathematical concepts, including representations and vector spaces and their relevance to quantum mechanics. The uses of symmetry properties and mathematical expression of symmetry operations are also outlined, along with symmetry transformations of the Hamiltonian. The next chapter describes the three uses of group theory, with particular reference to the theory of atomic energy levels and transitions. The following chapters deal with the theory of free atoms and ions; representations of finite groups; the electronic structure and vibrations of molecules; solid state physics; and relativistic quantum mechanics. Nuclear physics is also discussed, with emphasis on the isotopic spin formalism, nuclear forces, and the reactions that arise when the nuclei take part in time-dependent processes. This monograph will be of interest to physicists and mathematicians.

From Number Theory to Physics

Author : Michel Waldschmidt
Publisher : Springer Science & Business Media
ISBN 13 : 3662028387
Total Pages : 702 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis From Number Theory to Physics by : Michel Waldschmidt

Download or read book From Number Theory to Physics written by Michel Waldschmidt and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch.

Number Theory in Science and Communication

Author : Manfred Schroeder
Publisher : Springer Science & Business Media
ISBN 13 : 3540852972
Total Pages : 424 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Number Theory in Science and Communication by : Manfred Schroeder

Download or read book Number Theory in Science and Communication written by Manfred Schroeder and published by Springer Science & Business Media. This book was released on 2008-11-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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

Number Theory in Science and Communication

Author : Manfred R. Schroeder
Publisher : Springer Science & Business Media
ISBN 13 : 3662023954
Total Pages : 340 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Number Theory in Science and Communication by : Manfred R. Schroeder

Download or read book Number Theory in Science and Communication written by Manfred R. Schroeder and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Beauty is the first test: there is no permanent place in the world for ugly mathematics. " - G. H. Hardy N umber theory has been considered since time immemorial to be the very paradigm of pure (some would say useless) mathematics. In fact, the Chinese characters for mathematics are Number Science. "Mathematics is the queen of sciences - and number theory is the queen of mathematics," according to Carl Friedrich Gauss, the lifelong Wunderkind, who hirnself enjoyed the epithet "Princeps Mathematicorum. " What could be more beautiful than a deep, satisfying relation between whole numbers. {One is almost tempted to call them wholesome numbersJ In fact, it is hard to come up with a more appropriate designation than their learned name: the integers - meaning the "untouched ones". How high they rank, in the realms of pure thought and aesthetics, above their lesser brethren: the real and complex number- whose first names virtually exude unsavory involvement with the complex realities of everyday life! Yet, as we shall see in this book, the theory of integers can provide totally unexpected answers to real-world problems. In fact, discrete mathematics is ta king on an ever more important role. If nothing else, the advent of the digital computer and digital communication has seen to that. But even earlier, in physics the emergence of quantum mechanics and discrete elementary particles put a premium on the methods and, indeed, the spirit of discrete mathematics.

Quantum Theory for Mathematicians

Author : Brian C. Hall
Publisher : Springer Science & Business Media
ISBN 13 : 1461471168
Total Pages : 566 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Quantum Theory for Mathematicians by : Brian C. Hall

Download or read book Quantum Theory for Mathematicians written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2013-06-19 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Handbook of Number Theory in Quantum Mechanics

Author : N.B. Singh
Publisher : N.B. Singh
ISBN 13 :
Total Pages : 89 pages
Book Rating : 4./5 ( download)

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Book Synopsis A Handbook of Number Theory in Quantum Mechanics by : N.B. Singh

Download or read book A Handbook of Number Theory in Quantum Mechanics written by N.B. Singh and published by N.B. Singh. This book was released on with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Mathematics of Classical and Quantum Physics

Author : Frederick W. Byron
Publisher : Courier Corporation
ISBN 13 : 0486135063
Total Pages : 674 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Mathematics of Classical and Quantum Physics by : Frederick W. Byron

Download or read book Mathematics of Classical and Quantum Physics written by Frederick W. Byron and published by Courier Corporation. This book was released on 2012-04-26 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Theory and Quantum Mechanics

Author : Valter Moretti
Publisher : Springer
ISBN 13 : 331970706X
Total Pages : 950 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Spectral Theory and Quantum Mechanics by : Valter Moretti

Download or read book Spectral Theory and Quantum Mechanics written by Valter Moretti and published by Springer. This book was released on 2018-01-30 with total page 950 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Quantum Theory, Groups and Representations

Author : Peter Woit
Publisher : Springer
ISBN 13 : 3319646125
Total Pages : 659 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Quantum Theory, Groups and Representations by : Peter Woit

Download or read book Quantum Theory, Groups and Representations written by Peter Woit and published by Springer. This book was released on 2017-11-01 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Schrödinger Operators, Spectral Analysis and Number Theory

Author : Sergio Albeverio
Publisher : Springer Nature
ISBN 13 : 3030684903
Total Pages : 316 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Schrödinger Operators, Spectral Analysis and Number Theory by : Sergio Albeverio

Download or read book Schrödinger Operators, Spectral Analysis and Number Theory written by Sergio Albeverio and published by Springer Nature. This book was released on 2021-06-03 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory and Quantum Mechanics

Author : Michael Tinkham
Publisher : Courier Corporation
ISBN 13 : 0486131661
Total Pages : 354 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Group Theory and Quantum Mechanics by : Michael Tinkham

Download or read book Group Theory and Quantum Mechanics written by Michael Tinkham and published by Courier Corporation. This book was released on 2012-04-20 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids. The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.

Quantum Mechanics in Simple Matrix Form

Author : Thomas F. Jordan
Publisher : Courier Corporation
ISBN 13 : 0486137066
Total Pages : 274 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Quantum Mechanics in Simple Matrix Form by : Thomas F. Jordan

Download or read book Quantum Mechanics in Simple Matrix Form written by Thomas F. Jordan and published by Courier Corporation. This book was released on 2012-05-23 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Includes more than 100 problems and 38 figures. 1986 edition.

Noncommutative Geometry and Number Theory

Author : Caterina Consani
Publisher : Springer Science & Business Media
ISBN 13 : 3834803529
Total Pages : 374 pages
Book Rating : 4.8/5 (348 download)

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Book Synopsis Noncommutative Geometry and Number Theory by : Caterina Consani

Download or read book Noncommutative Geometry and Number Theory written by Caterina Consani and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Quantum Mechanics for Mathematicians

Author : Leon Armenovich Takhtadzhi͡an
Publisher : American Mathematical Soc.
ISBN 13 : 0821846302
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quantum Mechanics for Mathematicians by : Leon Armenovich Takhtadzhi͡an

Download or read book Quantum Mechanics for Mathematicians written by Leon Armenovich Takhtadzhi͡an and published by American Mathematical Soc.. This book was released on 2008 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.