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About 5,398 papers for “Inverse scattering problem”

The inverse scattering problem

Clayton, E · Research Online (University of Wollongong) · 1972

In scattering theory one assumes that the interaction between particles may be represented by a potential V(q,r) which in general is dependent on the velocity and separation of the particles. The problem of course is to determine that interaction. The traditional approach to this problem is to assume some form for the interaction, calculate cross sections, polarizations, etc., and then compare with experimental data. The interaction is then modified until agreement is reached. The inverse problem is posed in the opposite direction. Given information obtained from scattering experiments one tries directly to deduce the interparticle forces.

Cited by 0Open access

$q$-deformed inverse scattering problem

Hrubý, J. · Czech digital mathematics library · 1993

summary:Summary: Starting from the physical point of view on the Miura transformation as reflectionless potential and its connection with supersymmetry we define a scaling $q$-deformation of this to obtain $q$-deformed supersymmetric quantum mechanics. An application to an inverse scattering problem is given.

Cited by 0Open access

One-dimensional inverse scattering problem

P. K. Gaikovich, М. И. Сумин, К. П. Гайкович · 2011

The inverse problem of electromagnetic scattering of media with one-dimensional permittivity distribution is considered. Two approaches are applied in the study. First is based on the solution of non-linear integral equation for the scattered field; second-involves in analysis the Lagrange formalism applied to initial differential equations (Maxwell's equations). Based on the developed theory, solution algorithms have been worked out for diagnostics of subsurface permittivity inhomogeneities into multilayer periodic dielectric structures.

Cited by 11

The Electromagnetic Inverse Scattering Problem

Matteo Pastorino, J Bowman, A Communicated et al. · 2010

In this chapter the inverse scattering problem was considered which belongs to the category of inverse problems, which includes many very challenging problems encountered in several applications, including atmospheric sounding, seismology, heat conduction, quantum theory, and medical imaging. From a strictly mathematical perspective, the definition of a problem as the inverse counterpart of a direct one is completely arbitrary. In imaging applications, one measures the scattered field and tries to obtain information on the object subjected to the incident radiation. Computation of the electromagnetic field scattered by arbitrarily shaped dielectric objects when they are illuminated by a generic incident field is a complex task that seldom can be performed by using analytic techniques. Microwave imaging techniques can in principle be applied to three - dimensional configurations without theoretical limitations, most of the approaches proposed so far in the scientific literature are still related to two - dimensional problems. Controlled Vocabulary Terms dielectric materials; electromagnetic wave scattering; microwave imaging; radiation

Cited by 1Open access

Inverse Scattering Problem for Separable Potentials

Frank Tabakin · Physical Review · 1969

A method for constructing a separable potential directly from the two-nucleon phase shifts is presented. The solution of the inverse scattering problem is extended to include both a long-range attraction and the important strong, short-range repulsion. The occurrence of both an attraction and a strong repulsion in a single separable potential is shown to require that the phase shifts satisfy a modified Levinson theorem. Construction of a noncentral separable interaction directly from known eigenphase shifts and coupling parameters is also discussed. Using the construction procedure described in this paper, the task of repeated phase-shift fitting is avoided, and one can more easily test the sensitivity of nuclear structure calculations to various aspects of the two-nucleon interaction.

Cited by 49

Numerical solution to inverse scattering problem

А. Г. Рамм · 2025

A new method is given for the solution to inverse scattering problem. This method is based on the estimates of the solution to the Schrödinger equation. It is of interest to check the effectiveness of this method.

Cited by 0Open access

Inverse scattering problem for transparent obstacles

Vesselin Petkov · Mathematical Proceedings of the Cambridge Philosophical Society · 1982

Let K ⊂ ℝ 3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K . Set We wish to study the filtered scattering amplitude, related to the transmission problem Here w ± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω; . The function α(x) ∈ C ∞ ( K¯ ), called the index of refraction, has the property α( x ) > 0 for x ∈ K¯ .

Cited by 10