Non-Relativistic Quantum Dynamics
The bulk of known results in spectral and scattering theory for Schrodinger operators has been derived by time-independent (also called stationary) methods, which make extensive use of re solvent estimates and the spectral theorem. In very recent years t
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MA THEMA TICAL PHYSICS STUDIES A SUPPLEMENTARY SERIES TO LETTERS IN MATHEMATICAL PHYSICS
Editors:
D. ARNAL, Universite de Dijon, France M. FLA TO , Universite de Dijon, France M. GUENIN, Institut de Physique Theorique, Geneva, Switzerland R. RltczKA'/nstitute of Nuclear Research, Warsaw, Poland S. ULAM, University of Colorado, US.A. Assistant Editor:
J. C. Co R T E T, Universite de Dijon, France Editorial Board: H. ARAKI, Kyoto University, Japan A. O. BAR UT, University of Colorado, USA. J. P. ECKMANN, Institut de Physique Theorique, Geneva, Switzerland L. FAD D EE V, Steklov Institute of Mathematics, -Leningrad, USSR. C. FRONSDAL, UCLA, Los Angeles, USA. I. M. GELF AND, Moscow State University, USS.R. L. GROSS, Cornell University, USA. A. JAFFE, Harvard University, USA. J. P. JURZAK, Universite de Dijon, France M. KAC, The Rockefeller University, New York, USA. A. A. KIRILLOV ,Moscow State University, US.SR.
B. KOSTANT,M.I.T., US.A. A. LICHNEROWICZ, College de France, France E. H. LIEB, Princeton University, USA. B. NAG EL, K. T.H., Stockholm, Sweden
J. NIEDERLE,/nstitute of Physics CSA V, Prague, Czechoslovakia C. PIRON, Institut de Physique Theorique, Geneva, Switzerland A. SALAM, International Center for Theoretical Physics, Trieste, Italy I. E. SEGAL, M.I. T., USA. D. STERNHEIMER, College de France, France E. C. G. SUDARSHAN,University of Texas, US.A.
VOLUME 2
Non- Relativistic Quantum Dynamics by W. O. Amrein Department of Theoretical Physics, University of Geneva, Switzerland
D. Reidel Publishing Company Dordrecht, Holland / Boston, U.S.A. / London, England
Library of Congress Cataloging in Publication Data Amrein, Werner O. Non-relativistic quantum dynamics. (Mathematical physics studies; v. 2) Bibliography: p. Includes indexes. 1. Quantum theory. 2. Operator theory. I. Title. II. Series. QCI74.12.A48 530.1'2 81-10704 AACR2 ISBN 90-277-1324-3 (pbk.)
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TABLE OF CONTENTS vii
Preface CHAPTER 1 : LINEAR OPERATORS IN HILBERT SPACE 1.1 Hilbert Space
1 1
1.2 Linear Operators
10
1.3 Integration in Hilbert Space
21
CHAPTER 2 : SELF-ADJOINT OPERATORS. SCHRODINGER OPERATORS 2.1 Self-Adjointness Criteria
26
2.2 Spectral Properties of Self-Adjoint Operators
30
2.3 Multiplication Operators. The Laplacian
38
2.4 Perturbation Theory. Schrodinger Hamiltoni
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