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Mathematics for Quantum Mechanics

Mathematics for Quantum Mechanics Author John David Jackson
ISBN-10 9780486138817
Release 2012-03-08
Pages 112
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This concise text for advanced undergraduates and graduate students covers eigenvalue problems, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on functions, and linear vector spaces. 1962 edition.



Mathematics of Classical and Quantum Physics

Mathematics of Classical and Quantum Physics Author Frederick W. Byron
ISBN-10 9780486135069
Release 2012-04-26
Pages 672
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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.



Linear Operators for Quantum Mechanics

Linear Operators for Quantum Mechanics Author Thomas F. Jordan
ISBN-10 9780486140544
Release 2012-09-20
Pages 160
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Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.



Theory of Linear Operators in Hilbert Space

Theory of Linear Operators in Hilbert Space Author N. I. Akhiezer
ISBN-10 9780486318653
Release 2013-04-15
Pages 378
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This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.



Quantum Mechanics in Simple Matrix Form

Quantum Mechanics in Simple Matrix Form Author Thomas F. Jordan
ISBN-10 9780486137063
Release 2012-05-23
Pages 288
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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.



The Mathematical Principles of Quantum Mechanics

The Mathematical Principles of Quantum Mechanics Author Derek F. Lawden
ISBN-10 9780486442235
Release 2005
Pages 280
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Focusing on the principles of quantum mechanics, this text for upper-level undergraduates and graduate students introduces and resolves special physical problems with more than 100 exercises. 1967 edition.



A Modern Approach to Quantum Mechanics

A Modern Approach to Quantum Mechanics Author John S. Townsend
ISBN-10 1891389130
Release 2000-01-01
Pages 476
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This text allows lecturers to involve their undergraduates in the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound.



Linear Operator Theory in Engineering and Science

Linear Operator Theory in Engineering and Science Author Arch W. Naylor
ISBN-10 038795001X
Release 2000-02-23
Pages 624
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This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.



Applied Linear Algebra

Applied Linear Algebra Author Lorenzo Adlai Sadun
ISBN-10 9780821844410
Release 2007-12-20
Pages 371
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Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.



Mathematical Foundations of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics Author John von Neumann
ISBN-10 9781400889921
Release 2018-02-27
Pages 328
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Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.



Point Set Topology

Point Set Topology Author Steven A. Gaal
ISBN-10 9780486472225
Release 2009-04-23
Pages 336
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Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.



Sources of Quantum Mechanics

Sources of Quantum Mechanics Author B. L. Van Der Waerden
ISBN-10 9780486458922
Release 2007
Pages 430
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Originally published: Amsterdam: North-Holland Pub. Co., 1967.



Molecular Quantum Mechanics

Molecular Quantum Mechanics Author Peter W. Atkins
ISBN-10 9780199541423
Release 2011
Pages 537
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This text unravels those fundamental physical principles which explain how all matter behaves. It takes us from the foundations of quantum mechanics, through quantum models of atomic, molecular, and electronic structure, and on to discussions of spectroscopy, and the electronic and magnetic properties of molecules.



Quantum Mechanics in Hilbert Space

Quantum Mechanics in Hilbert Space Author Eduard Prugovecki
ISBN-10 9780486318059
Release 2013-07-02
Pages 720
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A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas. This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the gap between strictly physics- and mathematics-oriented texts on Hilbert space theory as applied to nonrelativistic quantum mechanics. Organized in the form of definitions, theorems, and proofs of theorems, it allows readers to immediately grasp the basic concepts and results. Exercises appear throughout the text, with hints and solutions at the end.



Quantum Theory Concepts and Methods

Quantum Theory  Concepts and Methods Author A. Peres
ISBN-10 9780306471209
Release 2006-06-01
Pages 450
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There are many excellent books on quantum theory from which one can learn to compute energy levels, transition rates, cross sections, etc. The theoretical rules given in these books are routinely used by physicists to compute observable quantities. Their predictions can then be compared with experimental data. There is no fundamental disagreement among physicists on how to use the theory for these practical purposes. However, there are profound differences in their opinions on the ontological meaning of quantum theory. The purpose of this book is to clarify the conceptual meaning of quantum theory, and to explain some of the mathematical methods which it utilizes. This text is not concerned with specialized topics such as atomic structure, or strong or weak interactions, but with the very foundations of the theory. This is not, however, a book on the philosophy of science. The approach is pragmatic and strictly instrumentalist. This attitude will undoubtedly antagonize some readers, but it has its own logic: quantum phenomena do not occur in a Hilbert space, they occur in a laboratory.



Lectures on Groups and Vector Spaces for Physicists

Lectures on Groups and Vector Spaces for Physicists Author C J Isham
ISBN-10 9789814507295
Release 1989-07-01
Pages 228
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These notes are the contents of a lecture course given to third year physics undergraduates at the Imperial College who are taking the theoretical physics option. The subject of “Algebra and Groups” is of considerable importance in a number of branches of modern theoretical physics, and therefore one major objective of the course is to introduce the students to the basic ideas on the subject, bearing in mind the potential applications to quantum theory. However, another equally important aim of the course is to introduce the student to the art of genuine “mathematical” thinking. The notes are therefore written in a more precise mathematical style than is usually the case in courses aimed at physics students. Quite apart from the general educational value of such an exposure to abstract thinking, it is also the case that much modern theoretical physics draws on sophisticated ideas from pure mathematics and therefore it is most important that a perspective graduate student can approach these subjects without experiencing a total culture shock! The course is divided into three parts. The first is a short introduction to general group theory, with particular emphasis being placed on the matrix Lie groups that play such a crucial role in modern theoretical physics. The second part deals with the theory of vector spaces, with particular attention being paid to the theory of Hilbert spaces and the basic analytical techniques that are needed to handle the infinite dimensional situation. The final part of the course is a short introduction to the theory of group representations and the associated theory of characters. Contents:GroupsVector SpacesGroup Representations Readership: Mathematical physicists and mathematicians.



The Principles of Quantum Mechanics

The Principles of Quantum Mechanics Author Paul Adrien Maurice Dirac
ISBN-10 0198520115
Release 1981-01-01
Pages 314
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The first edition of this work appeared in 1930, and its originality won it immediate recognition as a classic of modern physical theory. The fourth edition has been bought out to meet a continued demand. Some improvements have been made, the main one being the complete rewriting of the chapter on quantum electrodymanics, to bring in electron-pair creation. This makes it suitable as an introduction to recent works on quantum field theories.