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Atlantis Studies in Mathematical Physics: Theory and Applications

Lectures on the Mathematics of Quantum Mechanics II: Selected Topics

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
  • Directions for future research
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  • ISBN 978-94-6239-115-4
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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.

Table of contents (16 chapters)

Table of contents (16 chapters)
  • Lecture 1: Wigner Functions. Coherent States. Gabor Transform. Semiclassical Correlation Functions

    Pages 1-25

    Dell’Antonio, Gianfausto

  • Lecture 2: Pseudo-differential Operators. Berezin, Kohn–Nirenberg, Born–Jordan Quantizations

    Pages 27-50

    Dell’Antonio, Gianfausto

  • Lecture 3: Compact and Schatten Class Operators. Compactness Criteria. Bouquet of Inequalities

    Pages 51-81

    Dell’Antonio, Gianfausto

  • Lecture 4: Periodic Potentials. Wigner–Seitz Cell and Brillouen Zone. Bloch and Wannier Functions

    Pages 83-109

    Dell’Antonio, Gianfausto

  • Lecture 5: Connection with the Properties of a Crystal. Born–Oppenheimer Approximation. Edge States and Role of Topology

    Pages 111-131

    Dell’Antonio, Gianfausto

Buy this book

eBook 96,29 €
price for Spain (gross)
  • ISBN 978-94-6239-115-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 126,35 €
price for Spain (gross)
  • ISBN 978-94-6239-114-7
  • 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 II: Selected Topics
Authors
Series Title
Atlantis Studies in Mathematical Physics: Theory and Applications
Series Volume
2
Copyright
2016
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the author(s)
eBook ISBN
978-94-6239-115-4
DOI
10.2991/978-94-6239-115-4
Hardcover ISBN
978-94-6239-114-7
Series ISSN
2211-8055
Edition Number
1
Number of Pages
XIX, 381
Topics

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