Spectral Theory and Quantum Mechanics

With an Introduction to the Algebraic Formulation

  • ValterĀ Moretti

Part of the UNITEXT book series (UNITEXT)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT)

About this book

Introduction

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.

Keywords

Functional Analysis on Hilbert Spaces Mathematical Physics Quantum Mechanics Spectral Theory

Authors and affiliations

  • ValterĀ Moretti
    • 1
  1. 1.Department of MathematicsUniversity of TrentoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-88-470-2835-7
  • Copyright Information Springer-Verlag Italia 2013
  • Publisher Name Springer, Milano
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-88-470-2834-0
  • Online ISBN 978-88-470-2835-7
  • Series Print ISSN 2038-5714
  • About this book
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