The geometrical approach to multidimensional inverse scattering
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Publication:4873251
DOI10.1063/1.530937zbMath0849.35094OpenAlexW2031867899MaRDI QIDQ4873251
Publication date: 7 November 1996
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/82e1f6df2529166acecb148ca924b737ee776fe0
Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) (n)-body potential quantum scattering theory (81U10) Inverse scattering problems in quantum theory (81U40)
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Cites Work
- Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
- Propagation properties of quantum scattering states
- Inverse backscattering in two dimensions
- The existence of wave operators in scattering theory
- Inverse problem of quantum scattering theory. II
- Asymptotic completeness for quantum-mechanical potential scattering. II: singular and long-range potentials
- The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential
- A Multidimensional Inverse-Scattering Method
- Characterization of the scattering data in multidimensional inverse scattering theory
- The $ \bar\partial$-equation in the multidimensional inverse scattering problem
- Generalized limiting absorption method and multidimensional inverse scattering theory
- Global uniqueness at fixed energy in multidimensional inverse scattering theory
- On the uniqueness of inverse scattering for N-body systems
- An approximation formula in the inverse scattering problem
- The uniqueness theorem in the inverse problem of spectral analysis for the Schrödinger equation
- Multidimensional inverse scattering: the reconstruction problem
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