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Atlantis Studies in Mathematical Physics: Theory and Applications

Lectures on the Mathematics of Quantum Mechanics I

Authors: Dell'Antonio, Gianfausto

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  • Lecture notes in quantum mechanics
  • Advanced course on quantum mechanics
  • Mathematical approach to quantum mechanics
  • Course for advanced students in physics and mathematics
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  • ISBN 978-94-6239-118-5
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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 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.

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 non-relativistic 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)

Table of contents (20 chapters)
  • Lecture 1: Elements of the History of Quantum Mechanics I

    Pages 1-15

    Dell’Antonio, Gianfausto

  • Lecture 2: Elements of the History of Quantum Mechanics II

    Pages 17-37

    Dell’Antonio, Gianfausto

  • Lecture 3: Axioms, States, Observables, Measurement, Difficulties

    Pages 39-58

    Dell’Antonio, Gianfausto

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

    Pages 59-75

    Dell’Antonio, Gianfausto

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

    Pages 77-101

    Dell’Antonio, Gianfausto

Buy this book

eBook 96,29 €
price for Spain (gross)
  • ISBN 978-94-6239-118-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 126,35 €
price for Spain (gross)
  • ISBN 978-94-6239-117-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on the Mathematics of Quantum Mechanics I
Authors
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
978-94-6239-118-5
DOI
10.2991/978-94-6239-118-5
Hardcover ISBN
978-94-6239-117-8
Series ISSN
2211-8055
Edition Number
1
Number of Pages
XXI, 459
Topics

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