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  • © 1994

Mathematical Results in Quantum Mechanics

International Conference in Blossin (Germany), May 17–21, 1993

Birkhäuser

Part of the book series: Operator Theory: Advances and Applications (OT, volume 70)

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Table of contents (41 chapters)

  1. Front Matter

    Pages i-x
  2. Schrödinger and Dirac operators

    1. Front Matter

      Pages 1-1
    2. Regularity of the nodal sets of solutions to Schrödinger equations

      • M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, N. Nadirashvili
      Pages 19-25
    3. Stark ladders and perturbation theory

      • V. Grecchi, M. Maioli, A. Sacchetti
      Pages 33-36
    4. Singular potentials: Algebraization

      • Miloslav Znojil
      Pages 37-43
    5. Asymptotic Behavior of the Resolvent of the Dirac Operator

      • Chris Pladdy, Yoshimi Saitō, Tomio Umeda
      Pages 45-54
    6. Discrete spectrum of the perturbed Dirac operator

      • M. Sh. Birman, A. Laptev
      Pages 55-59
  3. Generalized Schrödinger operators

    1. Front Matter

      Pages 61-61
    2. A Fermi-type rule for contact embedded-eigenvalue perturbations

      • J.-P. Antoine, P. Exner, P. Šeba, J. Shabani
      Pages 79-87
    3. A Simple Model for Predissociation

      • P. Duclos, B. Meller
      Pages 89-105
    4. Scattering on Several Solenoids

      • Pavel Šťovíček
      Pages 107-112
    5. Hall conductance of Riemann surfaces

      • Markus Klein
      Pages 113-119
  4. Stochastic spectral analysis

    1. Front Matter

      Pages 121-121
    2. Framework and Results of Stochastic Spectral Analysis

      • Michael Demuth, Jan van Casteren
      Pages 123-132

About this book

The last decades have demonstrated that quantum mechanics is an inexhaustible source of inspiration for contemporary mathematical physics. Of course, it seems to be hardly surprising if one casts a glance toward the history of the subject; recall the pioneering works of von Neumann, Weyl, Kato and their followers which pushed forward some of the classical mathematical disciplines: functional analysis, differential equations, group theory, etc. On the other hand, the evident powerful feedback changed the face of the "naive" quantum physics. It created a contem­ porary quantum mechanics, the mathematical problems of which now constitute the backbone of mathematical physics. The mathematical and physical aspects of these problems cannot be separated, even if one may not share the opinion of Hilbert who rigorously denied differences between pure and applied mathemat­ ics, and the fruitful oscilllation between the two creates a powerful stimulus for development of mathematical physics. The International Conference on Mathematical Results in Quantum Mechan­ ics, held in Blossin (near Berlin), May 17-21, 1993, was the fifth in the series of meetings started in Dubna (in the former USSR) in 1987, which were dedicated to mathematical problems of quantum mechanics. A primary motivation of any meeting is certainly to facilitate an exchange of ideas, but there also other goals. The first meeting and those that followed (Dubna, 1988; Dubna, 1989; Liblice (in the Czech Republic), 1990) were aimed, in particular, at paving ways to East-West contacts.

Keywords

  • Generator
  • STATISTICA
  • operator theory
  • quantum mechanics
  • quantum physics
  • statistical physics

Editors and Affiliations

  • Technische Universität Clausthal, Institut für Mathematik, Clausthal-Zellerfeld, Germany

    M. Demuth

  • Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Moscow, Russia

    P. Exner

  • Fachbereich Mathematik MA 7-2, Technische Universität Berlin, Berlin, Germany

    H. Neidhardt

  • Université d’Aix-Marseille II et, Centre de Physique Théorique, Marseille Cedex 9, France

    V. Zagrebnov

Bibliographic Information

Buying options

eBook USD 74.99
Price excludes VAT (USA)
  • ISBN: 978-3-0348-8545-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.00
Price excludes VAT (USA)