Amrein W.O., Jauch J.M., Sinha K.B. Scattering Theory in Quantum Mechanics - Physical Principles and Mathematical Methods

London, Amsterdam: W. A. Benjamin Inc., 1977. — XXIII, 691 p. — (Lecture Notes and Supplements in Physics Series, Volume 16).Classic Text on Scattering Theory in Quantum Mechanics.Much of our knowledge about the physical world is derived from scattering experiments. Such experiments have led, for example, to the discoveries of the atomic nucleus, of nuclear fission, of new particles in modern accelerators and to the determination of the structure of crystals. The theoretical description of many of these phenomena is best given in the framework of quantum theory and is traditionally approached in one of the following three ways. The first one consists of studying solutions of the time-independent Schrodinger equation and of relating both the interaction and the scattering data to the asymptotic behaviour of such solutions at large distances. The second approach, the so-called stationary scattering theory, is an abstraction of the first one. This method had for a long time stayed on a formal level because of the difficulties in treating the continuous spectrum of the Hamiltonian. The last, and in our thinking the most satisfactory method, is the time-dependent one in which the temporal development of states and their behaviour in the remote past and the distant future plays the central role. These three methods of course describe the same physics and, from a purely mathematical point of view, they also lead to a determination of the spectral structure of certain self-adjoint operators, in particular the so-called Schrodinger operators.The purpose of this book is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods mentioned above and to derive the properties of various quantities of physical interest with mathematically rigorous methods. The book is designed for both physicists and mathematicians and can be used as a textbook in the physics or mathematics curriculum on the graduate level. It can also serve as an initiation to research in mathematical scattering theory.The presentation is mathematical in nature, and the principal results are given in the form of propositions. With few exceptions, complete proofs are provided. We use almost exclusively Hilbert space methods, sometimes at the expense of not obtaining the strongest possible result. Further results and some of the proofs omitted in the text are given in a section entitled "Notes and Supplementary Material", which is appended to many chapters and may be skipped in the first reading. The book also contains about 180 problems (many of them with a hint indicating a method of solution). They serve two purposes : to familiarize the reader with concepts and methods, and to supplement certain parts of the proofs in the text. Relatively difficult problems are marked with a dagger.Physical Heuristics
Hilbert Space and Linear Operators
One-Parameter Unitary Groups and Free Particles
Time-Dependent Scattering Theory
Spectral Theory of Self-Adjoint Operators
Time-Independent Scattering Theory
Position in Scattering Theory
Self-Adjointness. Existence of Wave Operators
Asymptotic Completeness
Eigenfunction Expansions
Spherical Symmetry in Scattering Theory
Scattering At High and At Low Energies
Scattering Theory for Long Range Potentials
General Formulation of Multichannel Scattering
Multichannel Potential Scattering
The Three-Body ProblemBibliography
Notation Index
Subject Index