A Mathematical Primer on Quantum Mechanics
A Mathematical Primer on Quantum Mechanics

Author: Alessandro Teta

Publisher: Springer

Published: 2018-04-17

Total Pages: 265

ISBN-13: 3319778935

DOWNLOAD EBOOK

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

Lectures on the Mathematics of Quantum Mechanics I
Lectures on the Mathematics of Quantum Mechanics I

Author: Gianfausto Dell'Antonio

Publisher: Springer

Published: 2015-05-25

Total Pages: 470

ISBN-13: 9462391181

DOWNLOAD EBOOK

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Hilbert Space Operators in Quantum Physics
Hilbert Space Operators in Quantum Physics

Author: Jirí Blank

Publisher: Springer Science & Business Media

Published: 2008-09-24

Total Pages: 677

ISBN-13: 1402088701

DOWNLOAD EBOOK

The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

Mathematical Methods in Quantum Mechanics
Mathematical Methods in Quantum Mechanics

Author: Gerald Teschl

Publisher: American Mathematical Soc.

Published: 2014-11-05

Total Pages: 378

ISBN-13: 1470417049

DOWNLOAD EBOOK

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrödinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrödinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. This new edition has additions and improvements throughout the book to make the presentation more student friendly.

Lectures on the Mathematics of Quantum Mechanics II: Selected Topics
Lectures on the Mathematics of Quantum Mechanics II: Selected Topics

Author: Gianfausto Dell'Antonio

Publisher: Springer

Published: 2016-05-24

Total Pages: 389

ISBN-13: 9462391157

DOWNLOAD EBOOK

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Solvable Models in Quantum Mechanics
Solvable Models in Quantum Mechanics

Author: S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, H. Holden, and an appendix by P. Exner

Publisher: American Mathematical Soc.

Published:

Total Pages: 508

ISBN-13: 9780821869406

DOWNLOAD EBOOK

"This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided. The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988."--Résumé de l'éditeur.

Operator Methods in Quantum Mechanics
Operator Methods in Quantum Mechanics

Author: Martin Schechter

Publisher: Courier Corporation

Published: 2014-06-10

Total Pages: 350

ISBN-13: 0486150046

DOWNLOAD EBOOK

This text introduces techniques related to physical theory. Entire book is devoted to a particle moving in a straight line; students develop techniques by answering questions about the particle. 1981 edition.

Solvable Models in Quantum Mechanics
Solvable Models in Quantum Mechanics

Author: Sergio Albeverio

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 458

ISBN-13: 3642882013

DOWNLOAD EBOOK

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.

The Many-Worlds Interpretation of Quantum Mechanics
The Many-Worlds Interpretation of Quantum Mechanics

Author: Bryce Seligman Dewitt

Publisher: Princeton University Press

Published: 2025-03-25

Total Pages: 329

ISBN-13: 0691273650

DOWNLOAD EBOOK

A landmark book on the influential many-worlds interpretation of quantum mechanics In 1957, Hugh Everett proposed a novel interpretation of quantum mechanics—a view that eventually became known as the many-worlds interpretation. This book presents Everett’s two landmark papers on the idea—“‘Relative State’ Formulation of Quantum Mechanics” and “The Theory of the Universal Wave Function”—as well as further discussion of the idea in papers from a number of other physicists: J. A. Wheeler, Bryce DeWitt, L. N. Cooper and D. Van Vechten, and Neill Graham. In his interpretation, Everett denies the existence of a separate classical realm and asserts the propriety of considering a state vector for the whole universe. Because this state vector never collapses, reality as a whole is rigorously deterministic. This reality, which is described jointly by the dynamical variables and the state vector, isn’t the reality customarily perceived; rather, it’s a reality composed of many worlds. By virtue of the temporal development of the dynamical variables, the state vector decomposes naturally into orthogonal vectors, reflecting a continual splitting of the universe into a multitude of mutually unobservable but equally real worlds, in each of which every good measurement has yielded a definite result, and in most of which the familiar statistical quantum laws hold. Bryce S. DeWitt (1923–2004) was a prize-winning theoretical physicist and professor emeritus of physics at the University of Texas at Austin. Neill Graham (1941–2015) was a physicist and writer.

Fundamental Principles of Molecular Modeling
Fundamental Principles of Molecular Modeling

Author: Anton Amann

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 247

ISBN-13: 1489902120

DOWNLOAD EBOOK

Molecular similarity has always been an important conceptual tool of chemists, yet systematic approaches to molecular similarity problems have only recently been recognized as a major contributor to our understanding of molecular properties. Advanced approaches to molecular similarity analysis have their foundation in quantum similarity measures, and are important direct or indirect contributors to some of the predictive theoretical, computational, and also experimental methods of modern chemistry. This volume provides a survey of the foundations and the contemporary mathematical and computational methodologies of molecular similarity approaches, where special emphasis is given to applications of similarity studies to a range of practical and industrially significant fields, such as pharmaceutical drug design. The authors of individual chapters are leading experts in various sub-fields of molecular similarity analysis and the related fundamental theoretical chemistry topics, as well as the relevant computational and experimental methodologies. Whereas in each chapter the emphasis is placed on a different area, nevertheless, the overall coverage and the wide scope of the book provides the reader with a general yet sufficiently detailed description that may serve as a good starting point for new studies and applications of molecular similarity approaches. The editors of this volume are grateful to the authors for their contributions, and hope that the readers will find this book a useful and motivating source of information in the rapidly growing field of molecular similarity analysis.