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Mathematical Results in Quantum Mechanics
Edited by: Ricardo Weder, IIMAS-UNAM, Mexico City, Mexico, Pavel Exner, Czech Academy of Sciences, Prague, Czech Republic, and Benoit Grébert, University of Nantes, France
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Contemporary Mathematics
2002; 350 pp; softcover
Volume: 307
ISBN-10: 0-8218-2900-9
ISBN-13: 978-0-8218-2900-4
List Price: US$103
Member Price: US$82.40
Order Code: CONM/307
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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.

Readership

Graduate students and research mathematicians interested in quantum mechanics.

Table of Contents

  • R. Adami -- Blow-up for Schrödinger equation with pointwise nonlinearity
  • J.-M. Barbaroux, M. Dimassi, and J.-C. Guillot -- Quantum electrodynamics of relativistic bound states with cutoffs. II
  • F. Bentosela and M. Tater -- Scattering by a slab: An exact calculation
  • X. Blanc and C. Le Bris -- Crystalline order in one dimensional Thomas-Fermi type models
  • J. Bourgain -- New results on the spectrum of lattice Schrödinger operators and applications
  • A. L. Bukhgeĭm, G. V. Dyatlov, and G. Uhlmann -- Reconstruction of the memory from partial boundary measurements
  • R. E. Cardiel and P. I. Naumkin -- Asymptotics for nonlinear dissipative equations in the super critical case
  • J.-M. Combes, P. D. Hislop, and E. Soccorsi -- Edge states for quantum Hall Hamiltonians
  • M. Combescure and D. Robert -- A semiclassical approach in linear response theory
  • J. Cruz-Sampedro -- Wigner-von Neumann-like potentials
  • M. Demuth and A. Noll -- Equilibrium potentials in scattering theory
  • J. Dittrich and J. Kříž -- Straight quantum waveguides with combined boundary conditions
  • V. Enss, V. Kostrykin, and R. Schrader -- Perturbation theory for the quantum time-evolution in rotating potentials
  • L. Erdős and V. Vougalter -- Two dimensional Pauli operator via scalar potential
  • M. J. Esteban and E. Séré -- A max-min principle for the ground state of the Dirac-Fock functional
  • S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and T. Sørensen -- On the regularity of the density of electronic wave functions
  • C. Hainzl -- Enhanced binding through coupling to a photon field
  • B. C. Hall and J. J. Mitchell -- The large radius limit for coherent states on spheres
  • I. Herbst and E. Skibsted -- Quantum scattering for potentials homogeneous of degree zero
  • W. Kirsch and I. Veselić -- Existence of the density of states for one-dimensional alloy-type potentials with small support
  • V. Kostrykin and R. Schrader -- Statistical ensembles and density of states
  • M. Kudryavtsev -- The Cauchy problem for the Toda lattice with a class of non-stabilized initial data
  • A. Laptev, S. Naboko, and O. Safronov -- Absolutely continuous spectrum of Jacobi matrices
  • E. H. Lieb and M. Loss -- Stability of matter in relativistic quantum electrodynamics
  • M. Măntoiu and R. Purice -- The algebra of observables in a magnetic field
  • D. B. Pearson -- Recent developments in value distribution theory for Schrödinger operators on the half line
  • D. Robert -- Long time propagation results in quantum mechanics
  • M. B. Ruskai -- Comments on adiabatic quantum algorithms
  • A. Sacchetti -- Tunneling destruction for a nonlinear Schrödinger equation
  • R. Seiringer -- Symmetry breaking in a model of a rotating Bose gas
  • S. B. Sontz -- Euler's constant in Segal-Bargmann analysis
  • A. Tip -- Maxwell with a touch of Schrödinger
  • J. H. Toloza -- Exponentially accurate semiclassical asymptotics
  • C. van der Mee and V. Pivovarchik -- Some properties of the eigenvalues of a Schrödinger equation with energy-dependent potential
  • C. Villegas-Blas -- The Bargmann transform for \(L^2(S^3)\) and regularization of the Kepler problem
  • K. Yajima and G. Zhang -- Schrödinger equations with superquadratic potentials
  • K. Yoshitomi -- Band spectrum of the Laplacian on a slab with the Dirichlet boundary condition on a grid
  • Other talks
  • Participants
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