Identification of Piecewise-Constant Potentials by Fixed-Energy Phase Shifts

Identification of Piecewise-Constant Potentials by Fixed-Energy Phase Shifts The 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. To resolve this difficulty we suggest the use of phase shifts corresponding to several energy levels. The identification is done by a nonlinear minimization of the appropriate objective function. It is based on a combination of probabilistic global and deterministic local minimization methods. The Multilevel Single-Linkage Method (MSLM) is used for the global minimization. A specially designed Local Minimization Method (LMM) with a Reduction Procedure is used for the local searches. Numerical results show the effectiveness of this procedure for potentials composed of a small number of spherical layers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Identification of Piecewise-Constant Potentials by Fixed-Energy Phase Shifts

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 2001 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-001-0010-1
Publisher site
See Article on Publisher Site

Abstract

The 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. To resolve this difficulty we suggest the use of phase shifts corresponding to several energy levels. The identification is done by a nonlinear minimization of the appropriate objective function. It is based on a combination of probabilistic global and deterministic local minimization methods. The Multilevel Single-Linkage Method (MSLM) is used for the global minimization. A specially designed Local Minimization Method (LMM) with a Reduction Procedure is used for the local searches. Numerical results show the effectiveness of this procedure for potentials composed of a small number of spherical layers.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2001

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