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The direct and inverse problem in Newtonian scattering*

Published online by Cambridge University Press:  14 November 2011

M. A. Astaburuaga ,
Claudio Fernández  and
Víctor H. Cortés
M. A. Astaburuaga
Affiliation:
Facultad de Matematicas, Pontificia Universidad Cató1ica de Chile, Casilla 6177, Santiago, Chile
Claudio Fernández
Affiliation:
Facultad de Matematicas, Pontificia Universidad Cató1ica de Chile, Casilla 6177, Santiago, Chile
Víctor H. Cortés
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
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Synopsis

In this paper we study the direct and inverse scattering problem on the phase space for a classical particle moving under the influence of a conservative force. We provide a formula for the scattering operator in the one-dimensional case and we settle the properties of the potential that can be deduced from it. We also study the question of recovering the shape of the barriers which can be seen from −∞ and ∞. An example is given showing that these barriers are not uniquely determined by the scattering operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 118 , Issue 1-2 , 1991 , pp. 119 - 131
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

1Astaburuaga, M. A., Cortés, V. and Fernández, C.. Non-autonomous classical scattering. J. Math. Anal. Appl. 134 (1988), 471–481.CrossRefGoogle Scholar
2Astaburuaga, M. A., Cortés, V. and Fernández, C.. Newtonian scattering in Hilbert space. J. Math. Anal. Appl. (in press).Google Scholar
3Cook, J.. Cargase Lectures in Theoretical Physics, ed. Lurchit, F. (New York: Gordon & Breach, 1967).Google Scholar
4Hunziker, W.. The S-matrix in classical mechanics. Comm. Math. Phys. 8 (1968), 282–299.Google Scholar
5Prosser, R.. On the asymptotic behavior of certain dynamical systems. J. Math. Phys. 13 (1972), 186–196.CrossRefGoogle Scholar
6Simon, B.. Wave operators for classical particle scattering. Comm. Math. Phys. 23 (1971), 37–48.Google Scholar
7Thirring, W.. Classical scattering theory. Acta Phys. Austriaca 23 (1981), 37–48.Google Scholar
8Narnhofer, H. and Thirring, W.. Canonical scattering transformation in classical mechanics. Phys. Rev. A 23 (1981), 1688–1697.CrossRefGoogle Scholar