La Matematica per il 3+2

Spectral Theory and Quantum Mechanics

With an Introduction to the Algebraic Formulation

Authors: Moretti, Valter

  • Most chapters are accompanied by exercises, many of which solved explicitly
  • At any rate several examples of the physical formalism are presented
  • Many of these aspects have been known for a long time but are scattered in the specialistic literature
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About this Textbook

This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged.

Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories.

In the attempt to reach out to Master's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.

About the authors

Valter Moretti serves as a Full Professor of Mathematical Physics at University of Trento (Italy). His research interests comprise rigorous quantum field theory in curved spacetime, mathematical aspects of quantum mechanics and general relativity, applications of operator algebras, functional analysis and global analysis to quantum field theory, and mathematical (analytic and geometric) methods for physics.

Reviews

From the reviews:

“The present text is an extended translation of its original Italian version published 2010 and gives a comprehensive introduction to the mathematical tools used in quantum mechanics. … The text is well-written and gives a self-contained and concise introduction to these topics. Many exercises make it suitable as a basis for various courses in this area.” (G. Teschl, Monatshefte für Mathematik, 2013)

Table of contents (14 chapters)

  • Introduction and mathematical backgrounds

    Moretti, Valter

    Pages 1-34

  • Normed and Banach spaces, examples and applications

    Moretti, Valter

    Pages 35-95

  • Hilbert spaces and bounded operators

    Moretti, Valter

    Pages 97-160

  • Families of compact operators on Hilbert spaces and fundamental properties

    Moretti, Valter

    Pages 161-207

  • Densely-defined unbounded operators on Hilbert spaces

    Moretti, Valter

    Pages 209-238

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-88-470-2835-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-88-470-2834-0
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Theory and Quantum Mechanics
Book Subtitle
With an Introduction to the Algebraic Formulation
Authors
Series Title
La Matematica per il 3+2
Copyright
2013
Publisher
Springer-Verlag Mailand
Copyright Holder
Springer-Verlag Italia
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-88-470-2835-7
DOI
10.1007/978-88-470-2835-7
Softcover ISBN
978-88-470-2834-0
Series ISSN
2038-5722
Edition Number
1
Number of Pages
XVI, 728
Topics