Number Theory In Quantum Mechanics

Author : N.B. Singh
Publisher : N.B. Singh
Page : 103 pages
File Size : 55,7 Mb
Release : 2024-06-23
Category : Science
ISBN : 8210379456XXX

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Number Theory in Quantum Mechanics by N.B. Singh Pdf

"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
Page : 89 pages
File Size : 41,7 Mb
Release : 2024-06-23
Category : Mathematics
ISBN : 8210379456XXX

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A Handbook of Number Theory in Quantum Mechanics by N.B. Singh Pdf

"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
Page : 424 pages
File Size : 44,6 Mb
Release : 2008-11-06
Category : Science
ISBN : 9783540852971

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Number Theory in Science and Communication by Manfred Schroeder Pdf

"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 : Sergio Albeverio,Anindita Balslev,Ricardo Weder
Publisher : Springer Nature
Page : 316 pages
File Size : 41,5 Mb
Release : 2021-06-03
Category : Mathematics
ISBN : 9783030684907

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Schrödinger Operators, Spectral Analysis and Number Theory by Sergio Albeverio,Anindita Balslev,Ricardo Weder Pdf

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 : Manfred R. Schroeder
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 43,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662023952

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Number Theory in Science and Communication by Manfred R. Schroeder Pdf

"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.

Author : Eugene P. Wigner
Publisher : Elsevier
Page : 384 pages
File Size : 51,5 Mb
Release : 2013-09-03
Category : Science
ISBN : 9781483275765

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Group Theory by Eugene P. Wigner Pdf

Group Theory and its Application to the Quantum Mechanics of Atomic Spectra describes the applications of group theoretical methods to problems of quantum mechanics with particular reference to atomic spectra. The manuscript first takes a look at vectors and matrices, generalizations, and principal axis transformation. Topics include principal axis transformation for unitary and Hermitian matrices; unitary matrices and the scalar product; linear independence of vectors; and real orthogonal and symmetric matrices. The publication also ponders on the elements of quantum mechanics, perturbation theory, and transformation theory and the bases for the statistical interpretation of quantum mechanics. The book discusses abstract group theory and invariant subgroups, including theorems of finite groups, factor group, and isomorphism and homomorphism. The text also reviews the algebra of representation theory, rotation groups, three-dimensional pure rotation group, and characteristics of atomic spectra. Discussions focus on eigenvalues and quantum numbers, spherical harmonics, and representations of the unitary group. The manuscript is a valuable reference for readers interested in the applications of group theoretical methods.

Author : George Whitelaw Mackey
Publisher : Addison Wesley Publishing Company
Page : 442 pages
File Size : 42,9 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:49015000884073

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Unitary Group Representations in Physics, Probability, and Number Theory by George Whitelaw Mackey Pdf

Author : Volker Heine
Publisher : Courier Corporation
Page : 663 pages
File Size : 44,8 Mb
Release : 2013-02-21
Category : Science
ISBN : 9780486174334

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Group Theory in Quantum Mechanics by Volker Heine Pdf

Geared toward research students in physics and chemistry, this text introduces the three main uses of group theory in quantum mechanics: (1) to label energy levels and the corresponding eigenstates; (2) to discuss qualitatively the splitting of energy levels, starting from an approximate Hamiltonian and adding correction terms; and (3) to aid in the evaluation of matrix elements of all kinds. "The theme," states author Volker Heine, "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." Early chapters cover symmetry transformations, the quantum theory of a free atom, and the representations of finite groups. Subsequent chapters address the structure and vibrations of molecules, solid state physics, nuclear physics, and relativistic quantum mechanics. A previous course in quantum theory is necessary, but the relevant matrix algebra appears in an appendix. A series of examples of varying levels of difficulty follows each chapter. They include simple drills related to preceding material as well as extensions of theory and further applications. The text is enhanced with 46 illustrations and 12 helpful appendixes.

Author : M. I. Petrashen,E. D. Trifonov,S. Chomet
Publisher : Courier Corporation
Page : 338 pages
File Size : 52,5 Mb
Release : 2009-03-01
Category : Science
ISBN : 9780486472232

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Applications of Group Theory in Quantum Mechanics by M. I. Petrashen,E. D. Trifonov,S. Chomet Pdf

Geared toward theoretical physicists, this advanced text explores the value of modern group-theoretical methods in quantum theory. It explains the theory of groups and their matrix representations, developing them to the level required for applications. The main focus rests upon point and space groups, with applications to electronic and vibrational states. 1969 edition.

Author : Michael Tinkham
Publisher : Courier Corporation
Page : 354 pages
File Size : 53,8 Mb
Release : 2003-12-17
Category : Science
ISBN : 9780486432472

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Group Theory and Quantum Mechanics by Michael Tinkham Pdf

Graduate-level text develops group theory relevant to physics and chemistry and illustrates their applications to quantum mechanics, with systematic treatment of quantum theory of atoms, molecules, solids. 1964 edition.

Author : Dennis A. Hejhal,Joel Friedman,Martin C. Gutzwiller,Andrew M. Odlyzko
Publisher : Springer Science & Business Media
Page : 693 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215448

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Emerging Applications of Number Theory by Dennis A. Hejhal,Joel Friedman,Martin C. Gutzwiller,Andrew M. Odlyzko Pdf

Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Author : Hermann Weyl
Publisher : Courier Corporation
Page : 468 pages
File Size : 54,7 Mb
Release : 1950-01-01
Category : Mathematics
ISBN : 0486602699

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The Theory of Groups and Quantum Mechanics by Hermann Weyl Pdf

This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.

Author : Takashi Aoki,Shigeru Kanemitsu,Mikio Nakahara,Yasuo Ohno
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 40,7 Mb
Release : 2008-05-10
Category : Mathematics
ISBN : 9780387249810

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Zeta Functions, Topology and Quantum Physics by Takashi Aoki,Shigeru Kanemitsu,Mikio Nakahara,Yasuo Ohno Pdf

This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.

Author : Bartel L. van der Waerden
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642658600

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Group Theory and Quantum Mechanics by Bartel L. van der Waerden Pdf

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 : Yair Shapira
Publisher : World Scientific
Page : 481 pages
File Size : 55,7 Mb
Release : 2022-06-24
Category : Science
ISBN : 9789811261794

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Set Theory And Its Applications In Physics And Computing by Yair Shapira Pdf

Why learn set theory? This book provides the answer — it is interesting, and also useful! Taking a new approach and looking from a fresh perspective, the discussion flows in a friendly and transparent way, supplemented with a lot of examples and figures. This makes the theory easily comprehensible: the proofs get vivid and visual, enveloped with interesting applications for students in (applied) math, physics, and engineering. Given the theory and the applications, the book could serve as a textbook in four (undergraduate) math courses: Introduction to set theory and its application; Chaos theory and stability — a geometrical point of view; Functional analysis — Han-Banach theory; and Cryptography with quantum computing. It teaches set theory from the basics, including the axiom of choice, the well ordering theorem, and Zorn's lemma. Furthermore, it uses Cantor's set to introduce chaos theory from a geometrical point of view. Moreover, it introduces the binomial formula (and other related formulas), and uses them in quantum statistical mechanics. And finally, it uses Zorn's lemma in functional analysis, general relativity, and quantum mechanics. There are also practical applications in cryptography, error correction, quantum computing and programming.