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Mathematical Methods in Physics

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

  • Philippe Blanchard
  • Erwin Brüning

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
    6. Philippe Blanchard, Erwin Brüning
      Pages 255-263
    7. Philippe Blanchard, Erwin Brüning
      Pages 265-276
    8. Philippe Blanchard, Erwin Brüning
      Pages 277-293
    9. Philippe Blanchard, Erwin Brüning
      Pages 295-305
    10. Philippe Blanchard, Erwin Brüning
      Pages 307-323
    11. Philippe Blanchard, Erwin Brüning
      Pages 325-342
    12. Philippe Blanchard, Erwin Brüning
      Pages 343-353
    13. Philippe Blanchard, Erwin Brüning
      Pages 355-363
    14. Philippe Blanchard, Erwin Brüning
      Pages 365-391
    15. Philippe Blanchard, Erwin Brüning
      Pages 393-417
    16. Philippe Blanchard, Erwin Brüning
      Pages 419-437
    17. Philippe Blanchard, Erwin Brüning
      Pages 439-453
    18. Philippe Blanchard, Erwin Brüning
      Pages 455-482
    19. Philippe Blanchard, Erwin Brüning
      Pages 483-500
  4. Variational Methods

    1. Front Matter
      Pages 501-501
    2. Philippe Blanchard, Erwin Brüning
      Pages 503-509
    3. Philippe Blanchard, Erwin Brüning
      Pages 511-517
    4. Philippe Blanchard, Erwin Brüning
      Pages 519-535
    5. Philippe Blanchard, Erwin Brüning
      Pages 537-546
    6. Philippe Blanchard, Erwin Brüning
      Pages 547-562
    7. Philippe Blanchard, Erwin Brüning
      Pages 563-573
  5. Back Matter
    Pages 575-597

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

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

Bibliographic information

  • 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
  • Print ISBN 978-3-319-14044-5
  • Online ISBN 978-3-319-14045-2
  • Series Print ISSN 1544-9998
  • Series Online ISSN 2197-1846
  • Buy this book on publisher's site
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