Mathematical Results in Quantum Mechanics

1. Front Matter

   Pages i-x

   PDF

2. Plenary talks

   1. Front Matter

      Pages 1-1

      PDF

   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

      PDF

   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

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.

• Analysis
• Mathematical physics
• Potential
• quantum mechanics
• scattering theory

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

  Jaroslav Dittrich, Pavel Exner, Miloš Tater

Policies and ethics