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A Schrödinger inverse scattering problem with a spectral dependence in the potential

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Abstract

The inverse scattering problem for the scalar Schrödinger equation \(y'' + \left[ {E - \sum\nolimits_{p = 0}^n {(\sqrt[{2n}]{E})^p } u_p (x)} \right]y = 0,{\text{ }}x \in \mathbb{R}\), is considered. It is solved by reduction to the inverse scattering problem for a matrix Schrödinger equation: \(Y'' + [EI - (U(x) + \sqrt E Q(x))]{\text{ }}Y = 0{\text{ }}x \in \mathbb{R}\).

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References

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Additional information

This work has been done as part of the program ‘Recherche Coopérative sur Programme No. 264: Etude interdisciplinaire des problèmes inverses’.

Physique Mathématique et Théorique, Equipe de recherche associée au CNRS, No. 154.

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Jaulent, M., Jean, C. A Schrödinger inverse scattering problem with a spectral dependence in the potential. Lett Math Phys 5, 183–190 (1981). https://doi.org/10.1007/BF00420697

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Keywords

  • Statistical Physic
  • Group Theory
  • Spectral Dependence
  • Scatter Problem
  • Inverse Scatter Problem