Titlebook: Inverse Problems in Quantum Scattering Theory; K. Chadan,P. C. Sabatier,R. G. Newton Book 1989Latest edition Springer-Verlag New York Inc.

HEDGE

Problems Connected with Discrete Spectra,showing a discrete spectrum, a continuous spectrum, and an exceptional spectrum; and there are also nonlinear systems exhibiting a generalized discrete spectrum. However, we shall stay with the “generic” (most simple) cases and their relations to quantum inverse scattering.

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Potentials from the Scattering Amplitude at Fixed Energy: Operator Methods,in the two first approaches given in this chapter. In the third approach, the combination of the two points of view enables one to answer all questions, but the scattering equivalent classes are large, and identifying special physical classes is still a problem.

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instate

Scattering Amplitudes from Elastic Cross Sections,solution of the problem. In typical situations, the scattering phase remains deeply involved in the formulas. Therefore, mathematical ways of constructing the scattering amplitude from the cross sections will be of interest for years.

DEMN

,The Gel’fand-Levitan-Jost-Kohn Method,that of Marchenko, which uses the Jost solution. It will be studied in the following chapters. Each one has its own advantages, and permits us to clarify some particular aspect of the problem. The two methods are of course equivalent to each other.

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Bravado

Miscellaneous Approaches to the Inverse Problems at Fixed ,ults are stated without proof and the reader who is interested in these proofs should refer to the literature. The notations are either the ones that are used elsewhere in this book or are specially given in each section.

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異端

Approximate Methods,?dinger equation, and one or several functions depending on the relative distance between the particles. Our “inverse problem” is the construction of these “potentials” from the experimental measurements.

JIBE

,Bound States—Eigenfunction Expansions, We are going to study them in detail because, as is well known, they are necessary in the completeness relation, and therefore, as was mentioned before, enter into the inverse problem. We again consider the .-wave first. The assumptions on the potential are those of the last section of chapter I :