Inverse scattering for a Schrödinger equation with energy dependent potential

@article{Mee2001InverseSF,
  title={Inverse scattering for a Schr{\"o}dinger equation with energy dependent potential},
  author={Cornelis Van der Mee and Vjacheslav Pivovarchik},
  journal={Journal of Mathematical Physics},
  year={2001},
  volume={42},
  pages={158-181}
}
In this article the inverse scattering problem of reconstructing the energy dependent potential iE2−m2 P(x)+Q(x) of a Schrodinger equation on the line from its reflection coefficients and bound state data (i.e., poles of the transmission coefficients and associated norming constants) is solved using the Marchenko integral equation approach. 

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References

SHOWING 1-10 OF 22 REFERENCES

Inverse scattering in one-dimensional nonconservative media

The inverse scattering problem arising in wave propagation in one-dimensional non-conservative media is analyzed. This is done in the frequency domain by considering the Schrödinger equation with the

A RIEMANN-HILBERT PROBLEM FOR AN ENERGY DEPENDENT SCHRODINGER OPERATOR

We consider an inverse scattering problem for Schr?dinger operators with energy-dependent potentials. The inverse problem is formulated as a Riemann - Hilbert problem on a Riemann surface. A

Asymptotics of the scattering coefficients for a generalized Schrödinger equation

The generalized Schrodinger equation d2ψ/dx2+F(k)ψ=[ikP(x)+Q(x)]ψ is considered, where P and Q are integrable potentials with finite first moments and F satisfies certain conditions. The behavior of

The inverses-wave scattering problem for a class of potentials depending on energy

AbstractThe inverse scattering problem is considered for the radials-wave Schrödinger equation with the energy-dependent potentialV+(E,x)=U(x)+2 $$\sqrt E $$ Q(x). (Note that this problem is closely

Wave scattering in one dimension with absorption

Wave scattering is analyzed in a one-dimensional nonconservative medium governed by the generalized Schrodinger equation d2ψ/dx2+k2ψ=[ikP(x)+Q(x)]ψ, where P(x) and Q(x) are real, integrable

Inverse scattering problems in absorbing media

We study inverse scattering problems which occur in various fields of physics (transmission lines theory, electromagnetism, elasticity theory), and in which the inhomogeneous media considered are

On the Inverse Problem for the Klein‐Gordon s‐Wave Equation

The s‐wave Klein‐Gordon equation of a particle in an electriclike, spherically symmetrical, local, and energy‐independent potential is studied with the aim of deriving exact relationships between the

The Inverse Problem for the One-Dimensional Schrodinger Equation with an Energy-Dependent Potential. 2.

The one-dimensional Schrodinger equation is considered when the potential V+(k, x) depends on the energy k2 in the following way : V+(k, x) = U(x) + 2kQ(x) ; (U(x), Q(x)) belongs to a large class 1/

Construction of potentials from phase shift and binding energies of relativistic equations

SummaryThe problem of constructing the potentialV(r) from givenS phase shift and binding energies of the Klein-Gordon equation is treated, and the analogue of the Gel’fand and Levitan integral

Finding Eigenvalue Problems for Solving Nonlinear Evolution Equations

The problem of determining what nonlinear evolution equations are exactly solvable by inverse scatte;ing techniques is simplified by considering a linear limit. By linearizing a given eigenvalue