000			02815 a2200265 4500
003			ISI Library, Kolkata
005			20240430114613.0
008			240430b |||||||| |||| 00| 0 eng d
020			_a9789819937035
040			_aISI Library _bEnglish
082	0	4	_223 _a530.124 _bIs85
100	1		_aIsozaki, Hiroshi
245	1	0	_aMany-body Schrodinger equation: _bscattering theory and eigenfunction expansions/ _cHiroshi isozaki
260			_aSingapore: _bSpringer Nature, _c2023
300			_axvii, 399 pages, _c24 cm.
490	0		_aMathematical Physics Studies
504			_aIncludes bibliography and index
505	0		_aSelf-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
520			_aSpectral 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 operators Compared 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.
650		4	_aPhysics
650		4	_aSchrodinger Equation
650		4	_aSchrodinger Operator
650		4	_aEigenfunction Expansion
942			_cBK _2ddc
999			_c433380 _d433380