Number Theory In Quantum Mechanics

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Group Theory And Quantum Mechanics

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Author : Bartel L. van der Waerden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Group Theory And Quantum Mechanics written by Bartel L. van der Waerden 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.

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.

Quantum Theory For Mathematicians

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Author : Brian C. Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-19

Quantum Theory For Mathematicians written by Brian C. Hall 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 2013-06-19 with Science categories.

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.

Group Theory And Quantum Mechanics

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Author : Michael Tinkham
language : en
Publisher: Courier Corporation
Release Date : 2012-04-20

Group Theory And Quantum Mechanics written by Michael Tinkham and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-20 with Science categories.

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 Theory Groups And Representations

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Author : Peter Woit
language : en
Publisher: Springer
Release Date : 2017-11-01

Quantum Theory Groups And Representations written by Peter Woit and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-01 with Science categories.

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.

Number Theory And Physics

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Author : Jean-Marc Luck
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Number Theory And Physics written by Jean-Marc Luck 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.

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.

Number Theory In Quantum Mechanics

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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :

Number Theory In Quantum Mechanics 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.

"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.

Mathematics Of Classical And Quantum Physics

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Author : Frederick W. Byron
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26

Mathematics Of Classical And Quantum Physics written by Frederick W. Byron and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Science categories.

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.

Group Theory In Quantum Mechanics

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Author : Volker Heine
language : en
Publisher: Elsevier
Release Date : 2014-05-15

Group Theory In Quantum Mechanics written by Volker Heine and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-15 with Science categories.

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.

Applications Of Group Theory In Quantum Mechanics

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Author : M. I. Petrashen
language : en
Publisher: Courier Corporation
Release Date : 2013-01-03

Applications Of Group Theory In Quantum Mechanics written by M. I. Petrashen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-03 with Science categories.

Geared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory. The authors based their text on a physics course they taught at a prominent Soviet university. Readers will find it a lucid guide to group theory and matrix representations that develops concepts to the level required for applications. The text's main focus rests upon point and space groups, with applications to electronic and vibrational states. Additional topics include continuous rotation groups, permutation groups, and Lorentz groups. A number of problems involve studies of the symmetry properties of the Schroedinger wave function, as well as the explanation of "additional" degeneracy in the Coulomb field and certain subjects in solid-state physics. The text concludes with an instructive account of problems related to the conditions for relativistic invariance in quantum theory.

An Introductory Path To Quantum Theory

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Author : Stephen Bruce Sontz
language : en
Publisher: Springer Nature
Release Date : 2020-03-16

An Introductory Path To Quantum Theory written by Stephen Bruce Sontz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-16 with Science categories.

Since the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics. The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.