# Inverse Scattering for a Schrï¿½dinger Operator with a Repulsive Potential

## Related Articles

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The one-dimensional matrix SchroÂ¨dinger equation is considered when the matrix potential is self-adjoint with entries that are integrable and have finite first moments. The small-energy asymptotics of the scattering coefficients are derived, and the continuity of the scattering coefficients...

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We construct a time-dependent scattering theory for SchrÃ¶dinger operators on a manifold M with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form â„Ã—âˆ‚M, where âˆ‚M is the boundary of M at...

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For a two-dimensional SchrÃ¶dinger operator H = âˆ’Î” âˆ’ Î±V with the radial potential V( x) = F(| x|), F( r) â‰¥ 0, we study the behavior of the number N( H) of its negative eigenvalues, as the coupling parameter Î± tends to infinity. We obtain the necessary and sufficient...

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construction of 'sparse potentials,' suggested by the authors for the lattice $ {\mathbb{Z}^d} $, d > 2, is extended to a large class of combinatorial and metric graphs whose global dimension is a number D > 2. For the SchrÃ¶dinger operator âˆ’ Î” âˆ’ Î±V on such graphs, with a...

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The matrix SchrÃ¶dinger equation with a self-adjoint matrix potential is considered on the half line with the most general self-adjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is...

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In this work are considered radial SchrÃ¶dinger operators -Ïˆâ€˜+V(r)Ïˆ=EÏˆ, where V(r)=a sin br/r+W(r) with W(r) bounded, W(r)=O(r-2) at infinity (a,b real). The asymptotic behavior of the Jost function and the scattering matrix near the resonance point E0=b2/4 are studied. If...

- Scattering on small three-dimensional, nonspherically symmetric potentials. Grinberg, N.I. // Journal of Mathematical Physics;Jun95, Vol. 36 Issue 6, p2702
Focuses on the scattering on small three-dimensional symmetric potentials modeled by the Schrodinger operator. Definition of the scattering amplitude (SA) given on the scattering of the plane wave; Correspondence between the scatterer and the SA; Production of a nonzero SA by nontrivial potential.

- A note on local behavior of eigenfunctions of the SchrÃ¶dinger operator. Ihyeok Seo // Journal of Mathematical Physics;2015, Vol. 56 Issue 6, p1
We show that a real eigenfunction of the SchrÃ¶dinger operator changes sign near some point in â„n under a suitable assumption on the potential.

- Scattering by a parabolic cylinderâ€”A uniform asymptotic expansion. Ott, R. H. // Journal of Mathematical Physics;Apr85, Vol. 26 Issue 4, p854
A uniform asymptotic expansion in the variable, determining the location of the observer for the fields scattered by a perfectly conducting parabolic cylinder, is derived. This expansion can be applied to scattering by arbitrary smooth convex surfaces of variable curvature. The accuracy of...