An algebraic method for solving the inverse problem of quantum scattering theory

2021/02/02 by N. A. Khokhlov, Khokhlov, N. A.
Engineering · Physics and Astronomy · #FOS: Physical sciences #Optical Polarization and Ellipsometry #Optical and Acousto-Optic Technologies #Photorefractive and Nonlinear Optics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2102.01464

openalex publication_date 2021/02/02 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28

Abstract

We present a new algebraic method for solving the inverse problem of quantum scattering theory based on the Marchenko theory. We applied a triangular wave set for the Marchenko equation kernel expansion in a separable form. The separable form allows a reduction of the Marchenko equation to a system of linear equations. For the zero orbital angular momentum, a linear expression of the kernel expansion coefficients is obtained in terms of the Fourier series coefficients of a function depending on the momentum q and determined by the scattering data on the finite range of q.

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