Mathematical Results in Quantum Mechanics: QMath7 Conference, Prague, June 22–26, 1998

Front Matter....Pages i-x
Front Matter....Pages 1-1
An Adiabatic Theorem without a Gap Condition....Pages 3-12
Two-Dimensional Periodic Pauli Operator. The Effective Masses at the Lower Edge of the Spectrum....Pages 13-31
Spectral Problems in the Theory of Photonic Crystals....Pages 33-46
Optimal Eigenvalues for Some Laplacians and Schrödinger Operators Depending on Curvature....Pages 47-58
The Spectral Shift Operator....Pages 59-90
On the scattering operator for the Schrödinger equation with a time-dependent potential....Pages 91-97
 H -2 —construction and some applications....Pages 99-105
Scattering with time periodic potentials and cyclic states....Pages 107-115
Some geometry related to decay properties of the resolvent of a class of symmetric operators....Pages 117-128
On Some Asymptotic Formulas in the Strong Localization Regime of the Theory of Disordered Systems....Pages 129-148
Spectral Measures and Category....Pages 149-159
Quantum dots....Pages 161-180
Front Matter....Pages 181-181
A Simple Model of Concentrated Nonlinearity....Pages 183-189
Anomalous electron trapping by magnetic flux tubes and electric current vortices....Pages 191-196
On the absolutely continuous energy distribution of a quantum mechanical system in a bounded domain....Pages 197-202
Some Aspects of Generalized Contact Interaction in One-Dimensional Quantum Mechanics....Pages 203-208
Traces and trace norms for semigroup differences....Pages 209-219
About a resolvent formula....Pages 221-226
The determinant anomaly in low-dimensional quantum systems....Pages 227-232
Linear Boltzmann Equation as the Weak Coupling Limit of the Random Schrödinger Equation....Pages 233-242
Front Matter....Pages 181-181
Coexistence of different spectral types for almost periodic Schrödinger equations in dimension one....Pages 243-251
Dynamical Localization for Random Schrödinger Operators and an Application to the Almost Mathieu Operator....Pages 253-257
On fractal structure of the spectrum for periodic point perturbations of the Schrödinger operator with a uniform magnetic field....Pages 259-265
A Weyl-Berry formula for the scattering operator associated to self-similar potentials on the line....Pages 267-274
Localization and Lifshitz tails for Random Quantum Waveguides....Pages 275-279
Birman-Schwinger Analysis for Bound States in a Pair of Parallel Quantum Waveguides with a Semitransparent Boundary....Pages 281-289
On absolute continuity of spectra of periodic elliptic operators....Pages 291-297
Hardy inequalities for magnetic Dirichlet forms....Pages 299-305
Adiabatic curvature, chaos and the deformations of Riemann Surfaces....Pages 307-314
Operator Interpretation of Resonances Arising in Spectral Problems for 2 x 2 Matrix Hamiltonians....Pages 315-322
On the operator-norm convergence of the Trotter-Kato product formula....Pages 323-334
A Particular Case of The Inverse Problem for The Sturm-Liouville Equation with Parameter-Dependent Potential....Pages 335-341
One-dimensional Schrödinger operators with decaying potentials....Pages 343-349
Stability of Limiting Absorption Principle under Singular Perturbations....Pages 351-357
Existence of Averaging Integrals for Self-Adjoint Operators....Pages 359-364
Monotonicity versus Non-Monotonicity in Random Operators....Pages 365-371
A model in perturbation theory....Pages 373-378
Band Gap of the Spectrum in Periodically Curved Quantum Waveguides....Pages 379-384
Back Matter....Pages 385-398