Tamas Palmai, Barnabas Apagyi
An inverse scattering method based on an auxiliary inverse Sturm-Liouville
problem recently proposed by Horv\'ath and Apagyi [Mod. Phys. Lett. B 22, 2137
(2008)] is examined in various aspects and developed further to (re)construct
spherically symmetric fixed energy potentials of compact support realized in
the three-dimensional Schr\"odinger equation. The method is generalized to
obtain a family of inverse procedures characterized by two parameters
originating, respectively, from the Liouville transformation and the solution
of the inverse Sturm-Liouville problem. Both parameters affect the bound states
arising in the auxiliary inverse spectral problem and one of them enables to
reduce their number which is assessed by a simple method. Various solution
techniques of the underlying moment problem are proposed including exact Cauchy
matrix inversion method, usage of spurious bound state and assessment of the
number of bound states. Examples include (re)productions of potentials from
phase shifts known theoretically or derived from scattering experiments.
View original:
http://arxiv.org/abs/1202.1931
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