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Ambiguities in the construction of potentials from phase shifts
Author(s) -
Sabatier Pierre C.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560070749
Subject(s) - semiclassical physics , ambiguity , uniqueness , phase (matter) , energy (signal processing) , point (geometry) , theoretical physics , statistical physics , physics , scattering , mathematics , quantum mechanics , mathematical analysis , computer science , geometry , quantum , programming language
An extensive study of ambiguities arising in the construction of potentials from phase shifts, given at a fixed energy, has been undertaken, and some of the results obtained, selected for their interest in theoretical chemistry and solid‐state physics, are presented. It is shown in particular that the semiclassical analysis of phase shifts, as more than one turning point is taken into account, yields a rather remarkable ambiguity: classes of equivalent potentials are layered almost shape independently. Another ambiguity, connected with the Born approximation, is also studied. It is hoped that this study will be used not only as a warning for uniqueness conjectures, but also to check rapidly other possible solutions of a scattering analysis.