Recovery of Compactly Supported Spherically Symmetric Potentials from the Phase Shift of the S-Wave

A. G. Ramm ()
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A. G. Ramm: Kansas State University, Department of Mathematics

Chapter 8 in Spectral and Scattering Theory, 1998, pp 111-130 from Springer

Abstract: 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.

Date: 1998
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DOI: 10.1007/978-1-4899-1552-8_8

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