1989•Physical Review LettersRequires access

Construction of the potential of the 3D Schrödinger equation from the scattering operator by using a Fredholm integral equation

Tuncay Aktosun, Cornelis van der Mee

Abstract

We consider the 3D Schr\"odinger equation with a potential having no spherical symmetry and show that such a potential can be constructed from the scattering operator by using the solution of a Fredholm integral equation. The Fredholm integral operator presented is compact and self-adjoint; its eigenvalues are symmetric about 0 and lie in [-1,1].

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Key concepts: Fredholm integral equation, Fredholm theory, Integral equation, Fredholm determinant, Operator (biology), Eigenvalues and eigenvectors, Scattering, Physics