{"product_id":"many-body-schrdinger-equation-hiroshi-isozaki-9789819937035","title":"Many-Body Schringer Equation: Scattering Theory and Eigenfunction Expansions","description":"Spectral properties for Schringer 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 \u003ci\u003eN\u003c\/i\u003e-body systems. The asymptotic completeness of time-dependent wave operators was proved in the 1980s and was a landmark in the study of the \u003ci\u003eN\u003c\/i\u003e-body problem. However, many problems are left open for the stationary \u003ci\u003eN\u003c\/i\u003e-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 \u003ci\u003eN\u003c\/i\u003e-body Schringer 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 \u003ci\u003eN\u003c\/i\u003e-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 Schringer operators-Time-dependent approach and stationary approach(3) Time-dependent approach to \u003ci\u003eN\u003c\/i\u003e-body Schringer operators(4) Eigenfunction expansion theory for three-body Schringer 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 Schringer 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 Schringer operators and standard knowledge for future development.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Hiroshi Isozaki\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9819937035\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789819937035\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/28\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 399\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.68lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.94d","brand":"Hiroshi Isozaki","offers":[{"title":"Hardcover","offer_id":44213064925439,"sku":"9789819937035","price":169.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_f0e0e392-4ff0-4bd8-aaa4-a63e22edc5fe.jpg?v=1692111867","url":"https:\/\/www.whiterainbookhouse.com\/products\/many-body-schrdinger-equation-hiroshi-isozaki-9789819937035","provider":"WR Book House","version":"1.0","type":"link"}