Abstract
It is proved that the phase shift δ0(k) known for all k > 0, determines a real-valued locally integrable spherically symmetric potential q(x), |q(x)| ≤ C exp(-c|x|γ), γ>1, where γ is a fixed number, c and C are positive constants. A procedure for finding the unknown potential from the above phase shift is proposed, an iterative process for finding the potential from the above data is described and its convergence is proved.
The author thanks R. Airapetyan for helpful discussions.
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Ramm, A.G. (1998). Recovery of Compactly Supported Spherically Symmetric Potentials from the Phase Shift of the S-Wave. In: Ramm, A.G. (eds) Spectral and Scattering Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1552-8_8
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DOI: https://doi.org/10.1007/978-1-4899-1552-8_8
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