Lectures on the Mathematics of Quantum Mechanics I
Authors: Dell'Antonio, Gianfausto
Free Preview Lecture notes in quantum mechanics
 Advanced course on quantum mechanics
 Mathematical approach to quantum mechanics
 Course for advanced students in physics and mathematics
Buy this book
 About this book

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 selfstudy 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, semiclassical analysis, quantum statistical mechanics. The structure of this book is suitable for a secondsemester 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.
 Reviews

“QM has also been the source of many interesting mathematical problems and developments to which only very few books devote careful attention and discussion. One of the praiseworthy merits of Dell'Antonio's book is to present a comprehensive and updates account of such important mathematical results. … For these reasons the book qualifies as a must for the education of mathematical physics graduate students and clearly provides very useful information also for theoretical physicists as well for mathematicians.” (Franco Strocchi, zbMATH 1357.81001, 2017)
“This is a huge book on the mathematical foundations of quantum theory, including both nonrelativistic quantum mechanics (QM) and quantum field theories (QFT). … the specialized reader will find in the book a very nice reference for checking concepts and ways of proceedings in these domains. It is a remarkable book.” (Décio Krause, Mathematical Reviews, May, 2016)
 Table of contents (20 chapters)


Lecture 1: Elements of the History of Quantum Mechanics I
Pages 115

Lecture 2: Elements of the History of Quantum Mechanics II
Pages 1737

Lecture 3: Axioms, States, Observables, Measurement, Difficulties
Pages 3958

Lecture 4: Entanglement, Decoherence, Bell’s Inequalities, Alternative Theories
Pages 5975

Lecture 5: Automorphisms; Quantum Dynamics; Theorems of Wigner, Kadison, Segal; Continuity and Generators
Pages 77101

Table of contents (20 chapters)
 Download Sample pages 2 PDF (216.4 KB)
 Download Table of contents PDF (243.2 KB)
Recommended for you
Bibliographic Information
 Bibliographic Information

 Book Title
 Lectures on the Mathematics of Quantum Mechanics I
 Authors

 Gianfausto Dell'Antonio
 Series Title
 Atlantis Studies in Mathematical Physics: Theory and Applications
 Series Volume
 1
 Copyright
 2015
 Publisher
 Atlantis Press
 Copyright Holder
 Atlantis Press and the author(s)
 eBook ISBN
 9789462391185
 DOI
 10.2991/9789462391185
 Hardcover ISBN
 9789462391178
 Series ISSN
 22118055
 Edition Number
 1
 Number of Pages
 XXI, 459
 Topics