Scattering for 1D Schrödinger equation with energy-dependent potentials and the recovery of the potential from the reflection coefficient. (English) Zbl 1050.81706

Aktosun, Tuncay; van der Mee, Cornelis

Phys. Rev. Lett. 65, No. 11, 1289-1293 (1990).

Summary: We consider the 1D Schrödinger equation with a potential proportional to energy. When the spatial part of the potential is twice continuously differentiable, is less than 1 everywhere, and satisfies a certain integrability condition, we compute the scattering matrix. For the same class of potentials, under the further assumption that the potential is non-negative, we obtain the potential from one of the reflection coefficients.

MSC:

81U05	\(2\)-body potential quantum scattering theory
34B30	Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
35J10	Schrödinger operator, Schrödinger equation
35P25	Scattering theory for PDEs
35R30	Inverse problems for PDEs

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