Piecewise constant positive potentials with practically the same fixed energy phase shifts
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چکیده
منابع مشابه
Piecewise-constant Positive Potentials with Practically the Same Fixed-energy Phase Shifts
It has recently been shown that spherically symmetric potentials of finite range are uniquely determined by the part of their phase shifts at a fixed energy level k > 0. However, numerical experiments show that two quite different potentials can produce almost identical phase shifts. It has been guessed by physicists that such examples are possible only for ”less physical” oscillating and chang...
متن کاملStable Identification of Piecewise-constant Potentials from Fixed-energy Phase Shifts
An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at any one fixed energy level. However, two different potentials can produce almost identical phase shifts. That is, the inverse problem of the identification of...
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An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at any one fixed energy level. However, two different potentials can produce almost identical phase shifts. That is, the inverse problem of the identification of...
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In this note we continue the study of the properties of phase shifts arising in the 3D inverse scattering with spherically symmetric potential. We provide various inequalities between the first two phase shift for some potential classes.
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No results of this type have been known or conjectured earlier. Condition (1.1) appeared in Müntz’s theorem: it is a necessary and sufficient condition for the completeness of the set {x} in L(0, a), for an arbitrary fixed a > 0. Such a result gives much deeper understanding of the quantum-mechanical inverse scattering problem with fixed-energy data. It may also be of some practical significanc...
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ژورنال
عنوان ژورنال: Applicable Analysis
سال: 2001
ISSN: 0003-6811,1563-504X
DOI: 10.1080/00036810108840933