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© 2015

Mathematical Methods in Physics

Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics

Textbook

Part of the Progress in Mathematical Physics book series (PMP, volume 69)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Distributions

    1. Front Matter
      Pages 1-1
    2. Philippe Blanchard, Erwin Brüning
      Pages 3-6
    3. Philippe Blanchard, Erwin Brüning
      Pages 7-24
    4. Philippe Blanchard, Erwin Brüning
      Pages 25-43
    5. Philippe Blanchard, Erwin Brüning
      Pages 45-61
    6. Philippe Blanchard, Erwin Brüning
      Pages 63-71
    7. Philippe Blanchard, Erwin Brüning
      Pages 73-84
    8. Philippe Blanchard, Erwin Brüning
      Pages 85-100
    9. Philippe Blanchard, Erwin Brüning
      Pages 101-117
    10. Philippe Blanchard, Erwin Brüning
      Pages 119-131
    11. Philippe Blanchard, Erwin Brüning
      Pages 133-162
    12. Philippe Blanchard, Erwin Brüning
      Pages 163-168
    13. Philippe Blanchard, Erwin Brüning
      Pages 169-179
    14. Philippe Blanchard, Erwin Brüning
      Pages 181-198
  3. Hilbert Space Operators

    1. Front Matter
      Pages 199-199
    2. Philippe Blanchard, Erwin Brüning
      Pages 201-212
    3. Philippe Blanchard, Erwin Brüning
      Pages 213-225
    4. Philippe Blanchard, Erwin Brüning
      Pages 227-238
    5. Philippe Blanchard, Erwin Brüning
      Pages 239-254

About this book

Introduction

The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas.  The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories.  All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods.

 

The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. Part II contains fundamental facts about Hilbert spaces and their geometry. The theory of linear operators, both bounded and unbounded, is developed, focusing on results needed for the theory of Schrödinger operators. Part III treats the direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. The appendices contain proofs of more general and deeper results, including completions, basic facts about metrizable Hausdorff locally convex topological vector spaces, Baire's fundamental results and their main consequences, and bilinear functionals. 

 

Mathematical Methods in Physics is aimed at a broad community of graduate students in mathematics, mathematical physics, quantum information theory, physics and engineering, as well as researchers in these disciplines. Expanded content and relevant updates will make this new edition a valuable resource for those working in these disciplines.

Keywords

Distribution theory Hilbert space operators Linear Operators Tensor products Variational methods

Authors and affiliations

  1. 1.Abt. Theoretische PhysikUniversität Bielefeld Fak. PhysikBielefeldGermany
  2. 2.School of Mathematics, Statistics, and Computer ScienceUniversity of KwaZulu-NatalDurbanSouth Africa

About the authors

Philippe Blanchard is Professor of Mathematical Physics at Bielefeld University in Germany. Erwin Bruening is a Research Fellow at the University of KwaZulu-Natal in South Africa.

Bibliographic information

  • Book Title Mathematical Methods in Physics
  • Book Subtitle Distributions, Hilbert Space Operators, Variational Methods, and Applications in Quantum Physics
  • Authors Philippe Blanchard
    Erwin Brüning
  • Series Title Progress in Mathematical Physics
  • Series Abbreviated Title Progress Mathemat.Physics(formerly:Progress in Physics)
  • DOI https://doi.org/10.1007/978-3-319-14045-2
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-14044-5
  • Softcover ISBN 978-3-319-37430-7
  • eBook ISBN 978-3-319-14045-2
  • Series ISSN 1544-9998
  • Series E-ISSN 2197-1846
  • Edition Number 2
  • Number of Pages XXVII, 598
  • Number of Illustrations 4 b/w illustrations, 0 illustrations in colour
  • Topics Mathematical Physics
    Mathematical Methods in Physics
    Functional Analysis
    Operator Theory
    Optimization
  • Buy this book on publisher's site
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Reviews

“This book gives a detailed survey on mathematical methods in physics … . The book is very suitable for students of physics, mathematics or engineering with a good background in analysis and linear algebra. … All in all, the book has a high didactical and scientific quality so that it can be recommended for both graduate students and researchers.” (Michael Demuth, zbMATH 1330.46001, 2016)