mathematical results in quantum mechanics · 2019. 2. 12. · mathematical results in quantum...
TRANSCRIPT
CONTEMPORARY MATHEMATICS
307
Mathematical Results in Quantum Mechanics
A Conference on QMATH-8, Mathematical Results in Quantum Mechanics
Universidad Nacional Aut6noma de Mexico, Taxco, Mexico December 10-14, 2001
Ricardo Weder Pavel Exner
Benoit Grebert Editors
Mathematical Results in Quantum Mechanics
http://dx.doi.org/10.1090/conm/307
QMath-8 Conference Participants
CoNTEMPORARY MATHEMATICS
307
Mathematical Results in Quantum Mechanics
A Conference on QMATH-8, Mathematical Results in Quantum Mechanics
Universidad Nacional Aut6noma de Mexico, Taxco, Mexico December 10-14, 2001
Ricardo Weder Pavel Exner
Benoit Grabert Editors
American Mathematical Society Providence, Rhode Island
Editorial Board Dennis DeThrck, managing editor
Andreas Blass Andy R. Magid Michael Vogelius
2000 Mathematics Subject Classification. Primary 35-06, 81-06, 92E99, 82D99, 81T99, 35P15, 35P25, 81Q10, 81Q15, 81U40.
Library of Congress Cataloging-in-Publication Data Mathematical results in quantum mechanics: proceedings of a conference on QMATH-8 mathe-matical results in quantum mechanics, December 1Q-14, 2001, Universidad Nacional Autonoma de Mexico, Taxco, Mexico/ Ricardo Weder, Pavel Exner, Benoit Grebert, editors.
p. em. -(Contemporary mathematics, ISSN 0271-4132; 307) Includes bibliographical references. ISBN 0-8218-2900-9 (alk. paper) 1. Quantum theory-Mathematical models-Congresses. 2. Mathematical physics-
Congresses. I. Weder, Ricardo, 1948- II. Exner, Pavel, 1946- III. Grebert, Benoit, 1965-IV. Contemporary mathematics (American Mathematical Society); v. 307.
QC173.96 .M382 2002 530.12---dc21 2002031161
Copying and reprinting. Material in this book may be reproduced by any means for edu-cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg-ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Acquisitions Department, American Math-ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to reprint-permission4lams.org.
Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.)
© 2002 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights
except those granted to the United States Government. Printed in the United States of America.
§ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability.
Visit the AMS home page at http: I /www. ams. org/
10 9 8 7 6 5 4 3 2 1 07 06 05 04 03 02
Contents
Preface IX
Blow-up for Schrodinger equation with pointwise nonlinearity R. ADAMI 1
Quantum electrodynamics of relativistic bound states with cutoffs. II J. M. BARBAROUX, M. DIMASSI, AND J. C. GUILLOT 9
Scattering by a slab: An exact calculation F. BENTOSELA AND M. TATER 15
Crystalline order in one dimensional Thomas-Fermi type models X. BLANC AND C. LE BRIS 21
New results on the spectrum of lattice Schrodinger operators and applications J. BOURGAIN 27
Reconstruction of the memory from partial boundary measurements A. L. BUKHEGEIM, G. v. DYATLOV, AND G. UHLMANN 39
Asymptotics for nonlinear dissipative equations in the super critical case R. E. CARDIEL AND P. I. NAUMKIN 47
Edge states for quantum Hall Hamiltonians J.-M. COMBES, P. D. HISLOP, AND E. SOCCORSI 69
A semiclassical approach in linear response theory M. COMBESCURE AND D. ROBERT 83
Wigner-von Neumann-like potentials J. CRUZ-SAMPEDRO 89
Equilibrium potentials in scattering theory M. DEMUTH AND A. NOLL 95
Straight quantum waveguides with combined boundary conditions J. DITTRICH AND J. KRIZ 107
Perturbation theory for the quantum time-evolution in rotating potentials V. ENSS, V. KOSTRYKIN, AND R. SCHRADER 113
Two dimensional Pauli operator via scalar potential L. ERDOS AND V. VOUGALTER 129
v
vi CONTENTS
A max-min principle for the ground state of the Dirac-Fock functional M. J. ESTEBAN AND E. SERE 135
On the regularity of the density of electronic wave functions S. FOURNAIS, M. HOFFMANN-0STENHOF, T. HOFFMANN-0STENHOF, AND T. 0STERGAARD S0RENSEN 143
Enhanced binding through coupling to a photon field C. HAINZL 149
The large radius limit for coherent states on spheres B. C. HALL AND J. J. MITCHELL 155
Quantum scattering for potentials homogeneous of degree zero I. HERBST AND E. SKIBSTED 163
Existence of the density of states for one-dimensional alloy-type potentials with small support W. KIRSCH AND I. VESELIC 171
Statistical ensembles and density of states V. KOSTRYKIN AND R. SCHRADER 177
The Cauchy problem for the Toda lattice with a class of non-stabilized initial data M. KUDRYAVTSEV 209
Absolutely continuous spectrum of Jacobi matrices A. LAPTEV, S. NABOKO, AND 0. SAFRONOV 215
Stability of matter in relativistic quantum electrodynamics E. H. LIEB AND M. LOSS 225
The algebra of observables in a magnetic field M. MANTOIU AND R. PURICE 239
Recent developments in value distribution theory for Schrodinger operators on the half line D. B. PEARSON 247
Long time propagation results in quantum mechanics D. ROBERT 255
Comments on adiabatic quantum algorithms M. B. RUSKAI 265
Tunneling destruction for a nonlinear Schrodinger equation A. SACCHETTI 275
Symmetry breaking in a model of a rotating Bose gas R. SEIRINGER 281
Euler's constant in Segal-Bargmann analysis S. B. SONTZ 287
Maxwell with a touch of Schrodinger A. TIP 293
CONTENTS vii
Exponentially accurate semiclassical asymptotics J. H. TOLOZA 299
Some properties of the eigenvalues of a Schrodinger equation with energy-dependent potential C. VANDER MEE AND V. PIVOVARCHIK 305
The Bargmann transform for £ 2 (83 ) and regularization of the Kepler problem C. VILLEGAS-BLAS 311
Schrodinger equations with superquadratic potentials K. YAJIMA AND G. ZHANG 319
Band spectrum of the Laplacian on a slab with the Dirichlet boundary condition on a grid K. YOSHITOMI 333
Other Talks 339
List of Participants 343
Preface
Quantum mechanics is a theory of a rich structure whose potential is far from exhausted. During its first decades the main areas of applications were in atomic and nuclear physics and through quantum field theory, also in the physics of el-ementary particles. More recently there is an emphasis in macroscopic quantum effects, condensed matter physics, and generally in areas of applied physics. The necessity of treating quantum systems from the first principles is not only a mathe-matician's desire for an "Ordnung", but it is increasingly important as the methods of studying quantum systems become more numerous and more complex.
The present volume collects some of the contributions presented at the confer-ence "QMath-8. Mathematical Results in Quantum Mechanics", held on December 10 - 14, 2001, at the facilities of Universidad Nacional Autonoma de Mexico, in Taxco, a fascinating colonial city of Mexico. There is also a paper by J. Bourgain, who was unable to attend, but submitted a manuscript.
Since the conference is the last one of a long series, it might be useful to recall briefly its history. It began in 1987 at the Laboratory of Theoretical Physics of the Joint Institute of Nuclear Research, in Dubna. The first meeting was small and topical, being devoted to applications of self-adjoint extensions in quantum physics. There was, at the time, the additional goal of finding new ways in which scientists from different parts of the world could collaborate. In the spring of 1990, the fourth conference met at the Liblice Castle near Prague. Under the new circumstances, it was decided to make the subject wider and to address all problems in quantum mechanics which can be studied by rigorous methods. Such a subject choice resonated within the community and the QMath series found a stable audience as the following meetings (Blossin 93, Ascona 96, and Prague 98) witnessed. With its eighth meeting, the series left Europe for the first time. Enough time has passed to look at the QMath series with some perspective. We believe that it plays a considerable role in the development of contemporary research in the mathematical physics of quantum mechanics, and we think that it can be already considered as a classical series of conferences.
The Taxco meeting was organized with the support of: Centro de Enseiianza para Extranjeros, Coordinacion de la Investigacion Cientifica, Direccion and Depar-tamento de Metodos Matematicos y Numericos of the Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Direccion General de Asuntos del Per-sonal Academico (project, Ecuaciones Diferenciales y Fisica Matematica, PAPIIT IN 105799), Direccion General de Servicios de Computo Academico, and Secretaria Administrativa; all of them from Universidad Nacional Autonoma de Mexico. We also had the support of Consejo Nacional de Ciencia y Tecnologia (project, In-vestigacion en Matematicas Aplicadas y su Enseiianza) and Sociedad Matematica
ix
X PREFACE
Mexicana. Several national science funds provided support for participants, in par-ticular the Czech and French ones. Last but not least, there was the hard work of the conference's secretary, Ana Mar!a Garda Ramirez, and the technical staff, Enrique Felipe Perez Garcia, Ricardo Federico Villarreal Martinez and Rodrigo Ca-margo Frias. We deeply thank them all for their support that made the success of QMath-8 possible.
At the same time, no conference can be successful without attentive participants who come with interesting talks and show activity in discussions. This was the case in Taxco, where we had a considerable number of young scientists, and we wish to thank all those who came, often a long way, and created an inspiring atmosphere. We are particularly grateful to the colleagues who have contributed to this volume and to the referees who reviewed the contributions rapidly but attentively.
Mexico, Nantes and Prague, June 2002
The editors
Other Talks
B. Apagyi: Potentials from phase shifts at fixed energies by a nonlinear inversion method
N. Atakishiyev: Mellin transforms for some families of q-polynomials
B. Bodmann: A transformation formula relating resolvents of Berezin-Toeplitz operators by an invariance property of Brownian motion
F. Brambila: Complete vectorial Radon transform
U. Carlsson: Schrodinger operators with several potential wells in the semiclassical limit
I. Catto: On the Hartre-Fock and Dirac-Fock models for crystals
R. del Rfo: Inverse spectral results for Dirac systems
Dong Shi-Hai: Ladder operator for the Morse potential
P. B. Espinoza: Moyal-like evolution equations for SU(2) quasi-distribution functions
P. Exner: A norm resolvent approximation of strongly singular interactions
Ch. Ferrari: Some spectral properties of finite quantum Hall systems
S. Fulling: The quantum theory of ceilings and floors
339
340 OTHER TALKS
A. Hinz: Delocalization for Schrodinger operators
M. Hitrik: Eigenfrequencies and expansions for dissipative wave equations
M. Horvath A necessary and sufficient condition in inverse eigenvalue problems
V. Ivrii: Functions on the box and logarithmic uncertainty principle
E. Kaikina: Asymptotic behaviour for Korteweg-de Vries-Burger equation on a half line without smallness initial data
M. Klaus: Spectral properties of the Zakharov-Shabat system and their implications for the propagation of optical pulses with chirp
M. Klein: Spectral theory and metastability for Markov chains
D. Krejcirik: Bound states in curved quantum layers
V. Kucherenko: Spectral asymptotics for the N particle Schrodinger equation with periodic binary potential
E. Ley-Koo: Variational theorem for the solutions of the many-electron relativistic quantum system
J. R. Mercado: Inverse problem for the similarity exponent
B. Mityagin: Counting lemma for lD periodic Dirac operator
F. Nicoleau: A scattering inverse problem with the Aharonov-Bohm effect
G. Panati: Space-adiabatic perturbation theory for the Dirac equation
G. S. Pogosyan: Coulomb-oscillator duality in spaces of constant curvature
OTHER TALKS 341
R. Quezada: A class of non-conservative quantum dynamics
V. Rabinovich: Pseudodifferential operators with analytic symbols and estimates for eigenfunc-tions of Schrodinger operators
G. Roepstorff: On a class of anomaly free gauge theories
D. Schumayer: Painleve test of coupled non-linear Schrodinger equations and Bose-Einstein condensation
H. Siedentop: The energy of relativistic one-electron atom
P. Stovicek: Weakly regular Floquet Hamiltonians with pure point spectrum
A. Strasburger: On the structure of the Weyl algebra and some families of orthogonal polyno-mials arising from various orderings
A. Turbiner: Canonical Discretization (discretization as canonical transformation)
K. B. Wolf: Finite quantum/optical systems
Participants
Aceff Flor de Marla Departamento de Matematicas, Facultad de Ciencias, UNAM Cd. Universitaria, C.P. 04510 D.F., Mexico [email protected]. unam.mx
Alonso y Coria Alberto I.F.E. Insurgentes Sur 1561, D.F. Mexico [email protected]
Apagyi Barnabas Budapest University of Technology and Economics Budafoki ut 8 H-1111 Budapest, Hungary apagyi@phy. bme.hu
Arredondo Juan Hector U AM, Iztapalapa Av. San Rafael Atlixco 186, Col. Vicentina, C.P. 09340 D.F. Mexico iva@xanum. uam.mx
Barbaroux Jean-Marie Departement de Mathematiques UMR 6629 du CNRS UMR, Faculte des Sciences et Techniques 2 rue de la Houssiniere 44322 Nantes Cedex 03, France barbarou@math. univ-nantes.fr
Adami Riccardo Departement de Mathematiques et Applications. Ecole Normale Superieure. 45 rue D'Ulm F75230 Paris cedex 05, Franc [email protected]
Angulo Carlos Ernesto CIMAT Callej6n Jalisco sjn, Valenciana Guanajuato, Mexico [email protected]
Arellano-Balderas Salvador Division C.B.I, UAM-Azcapotzalco Apdo. Postal16-306 02000 Mexico, D.F., Mexico [email protected]. uam.mx
Atakishiyev N atig Instituto de Matematicas, UNAM Apartado Postal 273-3, C.P. 62210 Cuernavaca, Mor., Mexico natig@matcuer. unam.mx
Barbosa Reyes Jesus Facultad de Ciencias, UNAM C.P. 04510, Cd. Universitaria, D.F., Mexico [email protected]. unam.mx
343
344 PARTICIPANTS
Bentosela Francois CNRS Case 907, 163 Av. de Luminy 13 288 Marseille Cedex 09, France bentosela@cpt. univ-mrs.fr
Bodmann Bernhard Department of Physics Princeton University 337 Jadwin Hall Princeton, NJ 08540, USA [email protected]
Brambila Paz Fernando Facultad de Ciencias, UNAM C.P. 04510, Cd. Universitaria, D.F. Mexico [email protected]. unam.mx
Catto Isabelle CNRS and CEREMADE University of Paris-Dauphine Place de Lattre de Tassigny 75775 Paris Cedex 16, France [email protected]
Chavez Jose Facultad de Ciencias, UNAM Circuito Escolar, Cd. Universitaria D.F., Mexico Josechr@eros. pquim. unam
Combescure Monique IPNL Batiment Paul Dirac Univ. Lyon 1 4 rue Enrico Fermi 69622 Villeurbanne, France [email protected]
Blancarte Herminio Facultad de Ingenierfa, Lie. en Matematicas Aplicadas Universidad Autonoma de Queretaro Queretaro, Qro., Mexico herbs@sunserver. uaq.mx
Bokanowski Olivier Universite Paris 7 UFR Mathematiques 16 rue clisson 75013 Paris, France [email protected]
Carlsson Ulf Department of Mathematics, Royal Institute of Technology 100 44 Stockholm, Sweden [email protected]
Cervera Pedro Facultad de Ciencias, UNAM Circuito Escolar, Cd. Universitaria D.F., Mexico [email protected]
Combes Jean Michel Universite de Toulon Toulon, France [email protected]
Cruz-Sampedro Jaime Instituto de Ciencias Basicas e Ingenierfa Universidad Autonoma de Hidalgo Carretera Pachuca-Thlancingo, Km. 4.5 42184 Pachuca, Hgo., Mexico [email protected]
PARTICIPANTS 345
Del Rio Rafael IIMAS, UNAM Circuito Escolar, Cd. Universitaria, C.P. 04510, D.F. Mexico delrio@servidor. unam.m.x
Demuth Michael Institut fuer Mathematik TU Clausthal Erzstrasse 1, 38678 Clausthal-Zellerfeld, Germany demuth@math. tu-clausthal.de
Dong Shi-Hai Instituto de Ciencias Nucleares UNAM Ciudad Universitaria, D.F. Mexico [email protected]
Enss Volker RWTH Aachen Aachen, Germany [email protected]
Exner Pavel Department of Theoretical Physics Institute for Nuclear Research Prague, Czech Republic [email protected]
Finco Domenico Mathematics Department, University La Sapienza Square A. Moro 5, 00185, Rome, Italy finco@mat. uniroma1.it
Fulling Stephen A. Mathematics Dept., Texas A&M University, College Station, TX, 77843-3368, USA fulling@math. tamu.edu
Delgado Cepeda Francisco Javier ITESM Campus Estado de Mexico Carr. Lago Guadalupe Km 3.5 Col. Margarita Maza de Juarez, Atizapan de Zaragoza, C.P. 52926, Estado de Mexico, Mexico [email protected]
Dittrich J aroslav Nuclear Physics Institute ASCR CZ-250 68 Rez, Czech Republic [email protected]
Ekholm Tomas Royal Institute of Technology Stockholm Sweden [email protected]
Espinoza Pedro Basilio Centro Universitario de los Altos Universidad de Guadalajara Lagos Moreno, Jalisco, Mexico [email protected]
Ferrari Christian Institut de Physique Theorique Dep. de Physique Swiss Federal Institute of Technology CH-1015 Lausanne, Switzerland christian. ferrari @epfl.ch
Fournais Soeren ESI Boltzmanngasse 9 A-1090 Wien, Austria [email protected]
Galvan Fernando Facultad de Medicina, UNAM Circuito Escolar, Cd. Universitaria, D.F., Mexico sabino@servidor. unam.m.x
346 PARTICIPANTS
Grebert Benoit Universite de Nantes Nantes, France [email protected]
Hainzl Christian LMU-Muenchen Institut fuer Mathematik LS Siedentop, Theresienstrasse 39 80333 Muenchen, Germany [email protected]. uni-muenchen.de
Herbst Ira Department of Mathematics University of Virginia Charlottesville, P.O. Box 400137 Virginia VA 22904-4137, USA [email protected]
Hernandez Curiel Idalia Instituto de Ciencias Basicas e Ingenieria Univ. Aut6noma del Estado de Hidalgo Carretera Pachuca-Thlancingo, Km. 4.5 Pachuca, Hidalgo, Mexico
Hitrik Michael Department of Mathematics University of California-Berkeley Berkeley, California 9472-3840 USA hitrik@math. berkeley.edu
I vrii Victor Department of Mathematics University of Toronto 100 St George Str. Toronto ON M5S3G3, Canada ivrii@math. toronto.edu
Klaus Martin Department of Mathematics Virginia Tech. Blacksburg, VA 24061, USA klaus@math. vt .edu
Guillot Jean-Claude Department of Mathematics, Institut Galilee, Universite Paris-Nord F-93430 Villetaneuse, France guillot@math. univ-paris13.fr
Hall Brian Department of Mathematics, University of Notre Dame 255 Hurley Building Notre Dame IN 46556-4618, USA [email protected]
Hernandez Orlando Mexico
Hinz Andreas Center for Mathematics Technical University D-80290 Munich, Germany hinz@appl-math. tu-muenchen.de
Horvath Miklos Department for Mathematical Analysis Budapest University of Technology and Economics Egry J6zsef u.1 H-1111 Budapest, Hungary horvath@math. bme.hu
Kaikina Elena Instituto Tecnol6gico de Morelia Morelia, Michoacan, Mexico pavelni@matmor. unam.mx
Klein Markus Department of Mathematics University Potsdam Am Neuen Palais 10 14469 Potsdam, Germany mklein@math. uni-potsdam.de
PARTICIPANTS 347
Krejcirik David Department of Theoretical Physics, Nuclear Institute, AS CR 25068 Rez near Prague, Czech Republic [email protected]
Kudryavtsev Mykhaylo IIMAS, UNAM Circuito Escolar, Cd. Universitaria 04510, D.F. Mexico [email protected] [email protected]
Le Bris Claude ENPC / Cermics 6/8 avenue Blaise Pascal, Cite Descartes, 77 455 Champs S/Marne, Marne la Valle cedex 2, France [email protected]
Lieb Elliot H. Princeton University Princeton, New Jersey, USA [email protected]
Marius Mantoiu Universite de Geneve, 24, Quai Ernest Ansermet, CH-1211 Geneve 4, Switzerland marius.mantoiu@physics. unige.ch
Me Dowell Stephen MSRI 1000 Centennial Drive Berkeley, CA, USA [email protected]
Mityagin Boris Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, Oh 43210, USA mityagin.l @osu.edu
Kucherenko Valeri Escuela Superior de Ffsica y Matematicas Instituto Politecnico Nacional Edificio 9, 3er piso, U .P. Adolfo Lopez Mateos, Col. Linda vista C.P. 07738, D.F., Mexico [email protected]
Laptev Ari Royal Institute of Technology Stockholm, Sweden [email protected]
Ley-Koo Eugenio Departamento de Ffsica Te6rica Instituto de Ffsica, UNAM Apdo. Postal 20-364 C.P. 01000, D.F., Mexico [email protected]. unam.mx
Lluis Puebla Emilio Sociedad Matematica Mexicana, Facultad de Ciencias, Edif. 0, Cd. Universitaria, C.P. 04510, D.F., Mexico
Martinez Teresa Facultad de Ciencias UNAM Circuito Escolar, Cd. Universitaria C.P. 04510, D.F. Mexico
Mercado-Escalante Jose Roberto Inst. Mex. de Tee. del Agua IMTA Paseo Cuauhnahuac 8532 62550, Jiutepec, Morelos, Mexico [email protected]
Muno Ralf Ruhr-Universitaet Bochum NA 3/27 44 780 Bochum, Germany ralf.muno@ruhr-uni. bochum.de
348 PARTICIPANTS
Naumkin Pavel I. U niversidad Michoacana Morelia, Mich. Mexico pavelni@matmor. unam.mx
Oestensson J oergen Royal Institute of Technology, Stockholm, Sweden [email protected]
Pearson David Department of Mathematics University of Hull Cottingham Road Hull Hu16 4RU, England [email protected]
Pita Ruiz Claudio de Jesus Centro de Inv. en Matematicas, A.C. Callejon de Jalisco, s/n Guanajuato, Gto., Mexico [email protected]
Quezada Roberto Departamento de Matematicas U. A. M.-Iztapalapa Av. San Rafael Atlixco No. 186, Col. Vicentina 09340, Iztapalapa D.F., Mexico roq b@xanum. uam.mx
Rico Juan Facultad de Ciencias, UNAM Circuito Escolar, Cd. Universitaria C.P. 04510, D.F., Mexico
Roepstorff Gert Institute for Theoretical Physics RWTH Aachen D-52062 Aachen, Germany [email protected]
Nicoleau Francois Universite de Nantes Departement de Mathematiques 2, rue de la Houssiniere BP 92208 F -44322 NANTES Cedex 03 France nicoleau@math. univ-nantes.fr
Panati Gianluca Mathematical Physics Sector, SISSA-ISAS Via Beirut 2-4 Trieste, Italy [email protected]
Perez Martinez Ricardo Escuela de Matematicas Universidad Autonoma de Coahuila Saltillo, Coah., Mexico rperez@mate. uadec.mx
Pogosyan George Centro de Ciencias Fisicas, UNAM Apdo. Postal 48-3 62251 Cuernavaca, Mor., Mexico pogosyan@fis. unam.mx
Rabinovitch Vladimir Depto. de Telecomunicaciones, ESIME-Zacatenco, IPN Av. IPN s/n Edif. 1 07738, D.F. Mexico [email protected]
Robert Didier Department of Mathematics, CNRS UMR University of Nantes 2 rue de la Houssiniere 44322-Nantes Cedex 03, France robert@math. univ-nantes.fr
Rojas Sandoval Daniel Universidad Autonoma del Estado de Hidalgo Pachuca, Hidalgo Mexico
PARTICIPANTS 349
Ruskai Mary Beth Department of Mathematics University of Massachusetts Lowell Lowell, MA 01854, USA [email protected]
Sandoval Romero Ma. de los Angeles liMAS, UNAM Circuito Escolar, Cd. Universitaria C.P. 04510, D.F. Mexico [email protected]
Schumayer Daniel Inst. of Physics, Dept. of Theoretical Physics Budapest University of Technology and Economics H-1111 Budafoki ut 8, Hungary daniel@eotvos. phy. bme.hu
Sere Eric CEREMADE Universite Paris 9 Place du Marechal de Lattre de Tassigny 75775 Paris Cedex 16, France [email protected]
Sontz Stephen CIMAT Callej6n de Jalisco s/n, Mineral de Valenciana Guanajuato, 36240 Guanajuato, Gto. Mexico [email protected]
Strasburger Aleksander Centre de Recherches Mathematiques Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, Quebec, H3C 3J7, Canada strasbur@CRM. U montreal.CA
Tater Milos Theory Department Nuclear Physics Institute, AS CR CZ-250 68 Rez, Czech. Republic [email protected]
Sacchetti Andrea Dipartimento di Matematica, Universita di Modena e Reggio Emilia, Via Campi 213/B 41100 Modena, Italy [email protected]
Schrader Robert Freie Universitaet Berlin Berlin, Germany [email protected]
Seiringer Robert Department of Physics Princeton University Jadwin Hall Princeton, NJ 08544, USA rseiring@ap. univie.ac.at
Siedentop H. Mathematik Theresienstr. 39 80333 Muenchen, Germany [email protected]. uni-muenchen.de
Stovicek Pavel Department of Mathematics, Czech Technical University Trojanova 13 120 00 Prague, Czech Republic [email protected]
Taneco Hernandez Marco Antonio Depto. de Ingenierfa y Tecnologfa Universidad Aut6noma de Tlaxcala Calzada de Apizaquito s/n Apizaco, Tlaxcala, Mexico [email protected]
Tchebotareva Olga liMAS, UNAM Circuito Escolar, Cd. Universitaria, 04510, D.F. Mexico [email protected]. unam.mx
350 PARTICIPANTS
Tip Adriaan FOM Instituut AMOLF Kruislaan 407 1098SJ Amsterdam, The Netherlands [email protected]
Tovar Leopolda Facultad de Ciencias, UNAM Circuito Escolar, Cd. Universitaria, 04510, D.F. Mexico [email protected]
Uhlmann Guenther University of Washington Seattle, Washington, USA gunther@math. washington.edu
Veselic Ivan Fakulta et fuer Mathematik Ruhr-Universitaet Bochum 44 780 Bochum, Germany I van. [email protected]
Vougalter Vitali Department of Mathematics The University of British Columbia Room 121, 1984 Mathematics Road Vancouver, B.C., V6T 1Z2, Canada vitali@math. ubc.ca
Wolf Kurt Bernardo Centro de Ciencias Ffsicas, UNAM Apartado Postal 48-3 62251 Cuernavaca, Mor., Mexico bwolf@fis. unam.mx
Yoshitomi Kazushi Graduate School of Mathematics, Kyushu University Hakosaki, Fukuoka 812-8581, Japan [email protected]
Toloza Julio Department of Physics Virginia Polytechnic Institute & State University Robeson Hall, Blacksburg,Virginia 24061-0435, USA jtoloza@quasar. phys. vt.edu
Turbiner A. Instituto de Ciencias Nucleares, UNAM Circuito Exterior, Cd. Universitaria 04510, D.F. Mexico turbiner@nuclecu. unam.mx
VanDer Mee Cornelis Dipartimento di Matematica, Universita di Cagliari Via Ospedale 72 09124 Cagliari, Italy [email protected]. unica.it
Villegas-Blas Carlos Instituto de Matematicas, UN AM Unidad Cuernavaca A.P. 273-3, Adm6n 3 Cuernavaca, Mor., Mexico [email protected]. unam.mx
Weder Ricardo IIMAS, UNAM Circuito Escolar, Cd. Universitaria, C.P. 04510, D.F., Mexico weder@servidor. unam.mx
Yajima Kenji University of Tokyo Tokyo, Japan yajima@ms. u-tokyo.ac.jp
Zuleta Luis Institut de Mathematiques BCH Universite de Laussanne Laussanne, Switzerland J oseL uis. Z uletaEstrugo@ima. unil. ch
This book contains contributions presented at the conference, "QMath-8: Mathematical Results in Quantum Mechanics", held at Universidap Nacional Aut6noma de Mexico 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 SchrOdinger 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.
ISBN 0-8218-2900-9
9 780821 829004
CONM/307