**Contemporary Mathematics**

Volume: 307;
2002;
350 pp;
Softcover

MSC: Primary 35; 81; 92; 82;

Print ISBN: 978-0-8218-2900-4

Product Code: CONM/307

List Price: $105.00

Individual Member Price: $84.00

**Electronic ISBN: 978-0-8218-7897-2
Product Code: CONM/307.E**

List Price: $105.00

Individual Member Price: $84.00

# Mathematical Results in Quantum Mechanics

Share this page *Edited by *
*Ricardo Weder; Pavel Exner; Benoit Grébert*

This book contains contributions presented at the conference, “QMath-8: Mathematical Results in Quantum Mechanics”, held at Universidad Nacional Autónoma de México in December 2001.

The articles cover a wide range of mathematical problems and focus on various aspects of quantum mechanics, quantum field theory, and nuclear physics. Topics vary from spectral properties of the Schrödinger equation of various quantum systems to the analysis of quantum computation algorithms.

The book is suitable for graduate students and research mathematicians interested in the mathematical aspects of quantum mechanics.

#### Table of Contents

# Table of Contents

## Mathematical Results in Quantum Mechanics

- Contents v6 free
- Preface ix10 free
- Blow-up for Schrödinger equation with pointwise nonlinearity 112 free
- Quantum electrodynamics of relativistic bound states with cutoffs. II 920
- Scattering by a slab: An exact calculation 1526
- Crystalline order in one dimensional Thomas-Fermi type models 2132
- New results on the spectrum of lattice Schrödinger operators and applications 2738
- Reconstruction of the memory from partial boundary measurements 3950
- Asymptotics for nonlinear dissipative equations in the super critical case 4758
- Edge states for quantum Hall Hamiltonians 6980
- A semiclassical approach in linear response theory 8394
- Wigner-von Neumann-like potentials 89100
- Equilibrium potentials in scattering theory 95106
- Straight quantum waveguides with combined boundary conditions 107118
- Perturbation theory for the quantum time-evolution in rotating potentials 113124
- Two dimensional Pauli operator via scalar potential 129140
- A max-min principle for the ground state of the Dirac-Fock functional 135146
- On the regularity of the density of electronic wave functions 143154
- Enhanced binding through coupling to a photon field 149160
- The large radius limit for coherent states on spheres 155166
- Quantum scattering for potentials homogeneous of degree zero 163174
- Existence of the density of states for one-dimensional alloy-type potentials with small support 171182
- Statistical ensembles and density of states 177188
- The Cauchy problem for the Toda lattice with a class of non-stabilized initial data 209220
- Absolutely continuous spectrum of Jacobi matrices 215226
- Stability of matter in relativistic quantum electrodynamics 225236
- The algebra of observables in a magnetic field 239250
- Recent developments in value distribution theory for Schrödinger operators on the half line 247258
- Long time propagation results in quantum mechanics 255266
- Comments on adiabatic quantum algorithms 265276
- Tunneling destruction for a nonlinear Schrödinger equation 275286
- Symmetry breaking in a model of a rotating Bose gas 281292
- Euler's constant in Segal-Bargmann analysis 287298
- Maxwell with a touch of Schrödinger 293304
- Exponentially accurate semiclassical asymptotics 299310
- Some properties of the eigenvalues of a Schrödinger equation with energy-dependent potential 305316
- The Bargmann transform for L2 (S3 ) and regularization of the Kepler problem 311322
- Schrödinger equations with superquadratic potentials 319330
- Band spectrum of the Laplacian on a slab with the Dirichlet boundary condition on a grid 333344
- Other Talks 339350
- List of Participants 343354

#### Readership

Graduate students and research mathematicians interested in quantum mechanics.