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Mathematical Results in Quantum Mechanics

QMath7 Conference, Prague, June 22–26, 1998

  • Conference proceedings
  • © 1999

Overview

Editors:
  1. Jaroslav Dittrich

    1. Department of Theoretical Physics, Nuclear Physics Institute Academy of Science, Rez near Prague, Czech Republic

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  2. Pavel Exner

    1. Department of Theoretical Physics, Nuclear Physics Institute Academy of Science, Rez near Prague, Czech Republic

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    You can also search for this editor in PubMed   Google Scholar

  3. Miloš Tater

    1. Department of Theoretical Physics, Nuclear Physics Institute Academy of Science, Rez near Prague, Czech Republic

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 108)

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Table of contents (38 papers)

  1. Front Matter

    Pages i-x
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  2. Plenary talks

    1. Front Matter

      Pages 1-1
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    2. An Adiabatic Theorem without a Gap Condition

      • J. E. Avron, A. Elgart
      Pages 3-12

    3. Two-Dimensional Periodic Pauli Operator. The Effective Masses at the Lower Edge of the Spectrum

      • M. Sh. Birman, T. A. Suslina
      Pages 13-31

    4. Spectral Problems in the Theory of Photonic Crystals

      • Jean-Michel Combes
      Pages 33-46

    5. Optimal Eigenvalues for Some Laplacians and Schrödinger Operators Depending on Curvature

      • Pavel Exner, Evans M. Harrell, Michael Loss
      Pages 47-58

    6. The Spectral Shift Operator

      • Fritz Gesztesy, Konstantin A. Makarov, Serguei N. Naboko
      Pages 59-90

    7. On the scattering operator for the Schrödinger equation with a time-dependent potential

      • Arne Jensen
      Pages 91-97

    8. H -2—construction and some applications

      • S. T. Kuroda, Hiroshi Nagatani
      Pages 99-105

    9. Scattering with time periodic potentials and cyclic states

      • Philippe A. Martin
      Pages 107-115

    10. Some geometry related to decay properties of the resolvent of a class of symmetric operators

      • E. Mourre
      Pages 117-128

    11. On Some Asymptotic Formulas in the Strong Localization Regime of the Theory of Disordered Systems

      • L. Pastur
      Pages 129-148

    12. Spectral Measures and Category

      • Rafael del Rio, Alexei Poltoratski
      Pages 149-159

    13. Quantum dots

      • Jakob Yngvason
      Pages 161-180

  3. Session talks

    1. Front Matter

      Pages 181-181
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    2. A Simple Model of Concentrated Nonlinearity

      • Riccardo Adami, Alessandro Teta
      Pages 183-189

    3. Anomalous electron trapping by magnetic flux tubes and electric current vortices

      • F. Bentosela, P. Exner, V. A. Zagrebnov
      Pages 191-196

    4. On the absolutely continuous energy distribution of a quantum mechanical system in a bounded domain

      • Johannes F. Brasche
      Pages 197-202

    5. Some Aspects of Generalized Contact Interaction in One-Dimensional Quantum Mechanics

      • Taksu Cheon, T. Shigehara
      Pages 203-208

    6. Traces and trace norms for semigroup differences

      • Michael Demuth
      Pages 209-219
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Keywords

About this book

At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de­ rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.

Editors and Affiliations

  • Department of Theoretical Physics, Nuclear Physics Institute Academy of Science, Rez near Prague, Czech Republic

    Jaroslav Dittrich, Pavel Exner, Miloš Tater

Bibliographic Information

  • Book Title: Mathematical Results in Quantum Mechanics

  • Book Subtitle: QMath7 Conference, Prague, June 22–26, 1998

  • Editors: Jaroslav Dittrich, Pavel Exner, Miloš Tater

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8745-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1999

  • Hardcover ISBN: 978-3-7643-6097-9Published: 01 April 1999

  • Softcover ISBN: 978-3-0348-9754-9Published: 02 November 2012

  • eBook ISBN: 978-3-0348-8745-8Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: X, 398

  • Topics: Mathematical Physics, Classical Mechanics

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