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New Estimates of the Potential Schrödinger Equation
Version 1
: Received: 22 March 2024 / Approved: 22 March 2024 / Online: 26 March 2024 (11:14:11 CET)
Version 2 : Received: 3 April 2024 / Approved: 3 April 2024 / Online: 4 April 2024 (12:35:41 CEST)
Version 2 : Received: 3 April 2024 / Approved: 3 April 2024 / Online: 4 April 2024 (12:35:41 CEST)
How to cite: Durmagambetov, A. New Estimates of the Potential Schrödinger Equation. Preprints 2024, 2024031417. https://doi.org/10.20944/preprints202403.1417.v2 Durmagambetov, A. New Estimates of the Potential Schrödinger Equation. Preprints 2024, 2024031417. https://doi.org/10.20944/preprints202403.1417.v2
Abstract
We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation
Keywords
Schrödinger equation; Poincaré–Riemann–Hilbert boundary-value problem; unitary scattering operator; quantum scattering theory
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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