Keywords
- Inverse Scattering
- Schrodinger Equation
- Spectral Projection
- Modern MathematicaL Physics
- Limit Absorption Principle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. G. Newton, Scattering Theory of Waves and Particles. 2nd edition. Springer, New York, 1982.
S. Agmon, "Spectral Properties of Schrödingers Operators and Scattering Theory," Annali della Scuola Norm. Sup. di Pisa, Classe di Science, Series IV, 2, 151–218 (1975).
M. Reed and B. Simon, Methods of Modern Mathematical Physics. I: Functional Analysis. Academic Press, New York, 1972.
E. G. Schmidt, "On the Representation of the Potential Scattering Operator in Quantum Mechanics," J. Diff. Eq. 7, 389–394 (1970).
P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, New York, 1967.
T. Kato, "Growth properties of solutions of the reduced wave equation with a variable coefficient," Comm. Pure and Appl. Math. 12. 403–425 (1959).
J. H. Rose, M. Cheney, and B. DeFacio, "Three-dimensional inverse scattering: Plasma and variable velocity wave equations," J. Math. Phys. 26, 2803–2813 (1985).
S. Coen, M. Cheney, and A. Weglein, "Velocity and density of a two-dimensional acoustic medium from point source surface data." J. Math. Phys. 25, 1857–1861 (1984).
M. Cheney, J. H. Rose, and B. DeFacio, "On the direct relation of the wavefield to the scattering amplitude," in preparation.
M. Schechter, Spectra of Partial Differential Operators, North-Holland, New York, 1971.
M. Reed and B. Simon, Methods of Modern Mathematical Physics. III: Scattering Theory, Academic Press, New York, 1979.
R. G. Newton, "Inverse Scattering. II. Three Dimensions," J. Math. Phys. 21, 1698–1715 (1980); 22, 631 (1981); 23, 693 (1982).
R. G. Newton, "Variational principles for inverse problems," Inverse Problems, 1, 371–380 (1985).
R. G. Newton, "Inverse Scattering, III. Three Dimensions, continued," J. Math. Phys. 22, 2191–2200 (1981); 23, 693 (1982).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Cheney, M., Rose, J.H., DeFacio, B. (1987). Three-dimensional inverse scattering. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080580
Download citation
DOI: https://doi.org/10.1007/BFb0080580
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18479-9
Online ISBN: 978-3-540-47983-3
eBook Packages: Springer Book Archive
