Mathematical Results in Quantum Mechanics

1. Front Matter

   Pages i-x

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2. Schrödinger and Dirac operators

   1. Front Matter

      Pages 1-1

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   2. Discrete spectrum of the periodic Schrödinger operator for non-negative perturbations

      • M. Sh. Birman

      Pages 3-7

   3. The discrete spectrum in a gap of the continuous one for compact supported perturbations

      • M. Sh. Birman, T. Weidl

      Pages 9-12

   4. Schrödinger Operators with Strong Local Magnetic Perturbations: Existence of Eigenvalues in Gaps of the Essential Spectrum

      • Rainer Hempel, Jörg Laitenberger

      Pages 13-18

   5. Regularity of the nodal sets of solutions to Schrödinger equations

      • M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, N. Nadirashvili

      Pages 19-25

   6. Results in the spectral theory of Schrödinger operators with wide potential barriers

      • Günter Stolz

      Pages 27-32

   7. Stark ladders and perturbation theory

      • V. Grecchi, M. Maioli, A. Sacchetti

      Pages 33-36

   8. Singular potentials: Algebraization

      • Miloslav Znojil

      Pages 37-43

   9. Asymptotic Behavior of the Resolvent of the Dirac Operator

      • Chris Pladdy, Yoshimi Saitō, Tomio Umeda

      Pages 45-54

   10. 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

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   2. The Spectrum of Schrödinger Operators in L _p (R ^d) and in C ₀(R ^d)

      • Rainer Hempel, Jürgen Voigt

      Pages 63-72

   3. On the spectral properties of generalized Schrödinger operators

      • J. F. Brasche

      Pages 73-78

   4. A Fermi-type rule for contact embedded-eigenvalue perturbations

      • J.-P. Antoine, P. Exner, P. Šeba, J. Shabani

      Pages 79-87

   5. A Simple Model for Predissociation

      • P. Duclos, B. Meller

      Pages 89-105

   6. Scattering on Several Solenoids

      • Pavel Šťovíček

      Pages 107-112

   7. Hall conductance of Riemann surfaces

      • Markus Klein

      Pages 113-119

4. Stochastic spectral analysis

   1. Front Matter

      Pages 121-121

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   2. Framework and Results of Stochastic Spectral Analysis

      • Michael Demuth, Jan van Casteren

      Pages 123-132

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.

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

• 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

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