Construction of a two-dimensional Schrödinger operator with given scattering amplitude at fixed energy (Q1820925)
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scientific article; zbMATH DE number 3996215
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Construction of a two-dimensional Schrödinger operator with given scattering amplitude at fixed energy |
scientific article; zbMATH DE number 3996215 |
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Construction of a two-dimensional Schrödinger operator with given scattering amplitude at fixed energy (English)
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1986
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The inverse scattering problem for the two-dimensional Schrödinger operator \(H=-\Delta +V(x,y)\) is considered. It is shown that the classical necessary properties of the scattering amplitude (duality and unitarity) are sufficient conditions for the existence of a decreasing potential with given scattering amplitude at fixed energy, if the \(L^ 2\) norm of the amplitude is small.
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inverse scattering problem
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two-dimensional Schrödinger operator
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scattering amplitude
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duality
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unitarity
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decreasing potential
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fixed energy
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