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

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,The Gel’fand-Levitan-Jost-Kohn Method, the radial Schrödinger equation, is that of Gel’fand and Levitan, and Jost and Kohn, and is the subject of the present chapter. The second method is 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 clar

guzzle

exceptional

Examples,.. In fact, in the third section of chapter IV we studied an even more general case consisting of an initial arbitrary potential for which everything is known, and an increment which has the effect of multiplying the initial Jost function by a rational function of ..

hieroglyphic

Special Classes of Potentials,roblem for them can be dealt with either by the Gel’fand-Levitan or by the Marchenko method, a special technique has been found by Martin which permits solving the direct as well as the inverse problem by an iterative method based on special properties of the Laplace transform. We follow his method.

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deriver

Scattering Amplitudes from Elastic Cross Sections,relations on scattered particles at different space-time points. The interest of such measurements has been pointed out by Goldberger et al. (1963, 1964, 1965, 1966), following Hanbury Brown and Twiss (1954, 1956). They proved that, with this technique, it is possible to explicitly measure the phase

rheumatism

Potentials from the Scattering Amplitude at Fixed Energy: General Equation and Mathematical Tools,θ) has been constructed from the cross section. The next step in studying the interaction is to introduce a mathematical model in which the interaction appears as a parameter, and to determine that parameter from ., cos θ). Such is the Schrödinger equation with a spherically symmetric potential . in

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Potentials from the Scattering Amplitude at Fixed Energy: Operator Methods,view is to define a certain large class of functions . and then try to answer the questions of section XI.1 (existence, uniqueness, construction ...) in this class. In the first kind of approach, one risks obtaining potentials that violate certain fine physical requirements. In the second kind, one