# 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.

## 23 Citations

### Inverse scattering problem for the Schrödinger-type equation with a polynomial energy-dependent potential

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In the present paper the inverse scattering problem for the Schrödinger-type equation with a polynomial energy-dependent potential is investigated on the entire real line (−∞; + ∞). The scattering…

### Energy Dependent Inverse Scattering

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### Inverse scattering on the half-line for energy-dependent Schrödinger equations

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### INVERSE SCATTERING PROBLEM FOR THE ·IMPULSIVE SCHRÖDINGER EQUATION WITH A POLYNOMIAL SPECTRAL DEPENDENCE IN THE POTENTIAL

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In the present work, under some di¤erentiability conditions on the potential functions , we
rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to…

### INVERSE SCATTERING PROBLEMS FOR ENERGY-DEPENDENT STURM-LIOUVILLE EQUATIONS WITH POINT δ-INTERACTION AND EIGENPARAMETER-DEPENDENT BOUNDARY CONDITION

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- 2013

We consider an inverse problem of the scattering theory for energydependent Sturm-Liouville equations on the half line [0,+∞) with point δinteraction and eigenparameter-dependent boundary condition.…

### Generalized Schrödinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class

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- 2020

We construct Darboux transformations of arbitrary order for generalized Schrodinger-type equations, the potentials of which are second-degree polynomials in the energy. Our equations are allowed to…

### Inverse Scattering on the Half-Line for ZS-AKNS Systems with Integrable Potentials

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In this paper, we study the inverse scattering problem for ZS-AKNS systems on the half-line with general boundary conditions at the origin. For the class of potentials with certain integrability…

### Inverse Scattering on the Half-Line for ZS-AKNS Systems with Integrable Potentials

- MathematicsIntegral Equations and Operator Theory
- 2015

In this paper, we study the inverse scattering problem for ZS-AKNS systems on the half-line with general boundary conditions at the origin. For the class of potentials with certain integrability…

### Integral Representations for the Solutions of the Generalized Schroedinger Equation in a Finite Interval

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We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful…

### Reconstruction of Energy-Dependent Sturm–Liouville Equations from two Spectra

- Mathematics
- 2012

In this paper we study the inverse spectral problem of reconstructing energy-dependent Sturm–Liouville equations from two spectra. We give a reconstruction algorithm and establish existence and…

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