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.Â
General
Imprint: |
Springer Verlag, Singapore
|
Country of origin: |
Singapore |
Series: |
Mathematical Physics Studies |
Release date: |
September 2023 |
First published: |
2023 |
Authors: |
Hiroshi Isozaki
|
Dimensions: |
235 x 155mm (L x W) |
Pages: |
399 |
Edition: |
1st ed. 2023 |
ISBN-13: |
978-981-9937-03-5 |
Categories: |
Books
|
LSN: |
981-9937-03-5 |
Barcode: |
9789819937035 |
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