Many-Body Schrödinger Equation

Scattering Theory and Eigenfunction Expansions

Hiroshi Isozaki (Autor)

Buch | Softcover

399 Seiten

2024 | 2023 ed.
Springer Verlag, Singapore
978-981-99-3706-6 (ISBN)

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Spectral properties for Schrödinger operators are a major concern in quantum mechanics both in physics and in mathematics. For the few-particle systems, we now have sufficient knowledge for two-body systems, although much less is known about N-body systems. The asymptotic completeness of time-dependent wave operators was proved in the 1980s and was a landmark in the study of the N-body problem. However, many problems are left open for the stationary N-particle equation. Due to the recent rapid development of computer power, it is now possible to compute the three-body scattering problem numerically, in which the stationary formulation of scattering is used. This means that the stationary theory for N-body Schrödinger operators remains an important problem of quantum mechanics. It is stressed here that for the three-body problem, we have a satisfactory stationary theory. This book is devoted to the mathematical aspects of the N-body problem from both the time-dependent and stationary viewpoints. The main themes are:(1) The Mourre theory for the resolvent of self-adjoint operators(2) Two-body Schrödinger operators-Time-dependent approach and stationary approach(3) Time-dependent approach to N-body Schrödinger operators(4) Eigenfunction expansion theory for three-body Schrödinger operatorsCompared with existing books for the many-body problem, the salient feature of this book consists in the stationary scattering theory (4). The eigenfunction expansion theorem is the physical basis of Schrödinger operators. Recently, it proved to be the basis of inverse problems of quantum scattering. This book provides necessary background information to understand the physical and mathematical basis of Schrödinger operators and standard knowledge for future development.

Self-Adjoint Operators and Spectra.- Two-Body Problem.- Asymptotic Completeness for Many-Body Systems.- Resolvent of Multi-Particle System.- Three-Body Problem and the Eigenfunction Expansion.- Supplement.

Erscheinungsdatum	31.07.2024
Reihe/Serie	Mathematical Physics Studies
Zusatzinfo	10 Illustrations, black and white; XVII, 399 p. 10 illus.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Algebra of commutators • asymptotic completeness • Eigenfunction expansion theory • Mourre theory • radiation condition
ISBN-10	981-99-3706-X / 981993706X
ISBN-13	978-981-99-3706-6 / 9789819937066
Zustand	Neuware