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SIAM Review

Scattering Theory by the Enss Method (Peter A. Perry) (B. Simon, ed.)

George A. Hagedorn

Published Jun 1, 1985• 2 citations

Abstract

Previous article Next article Scattering Theory by the Enss Method (Peter A. Perry) (B. Simon, ed.)George A. HagedornGeorge A. Hagedornhttps://doi.org/10.1137/1027082PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Scattering Theory by the Enss Method (Peter A. Perry) (B. Simon, ed.)." SIAM Review, 27(2), pp. 274–275[1] Volker Enss, Asymptotic completeness for quantum mechanical potential scattering. I. Short range potentials, Comm. Math. Phys., 61 (1978), 285–291 58:25583 0389.47005 CrossrefISIGoogle Scholar[2] Volker Enss, P. Blanchard, Completeness of three-body quantum scatteringDynamics and processes (Bielefeld, 1981), Lecture Notes in Math., Vol. 1031, Springer, Berlin, 1983, 62–88, Heidelberg–New York 85h:81071 0531.47009 CrossrefGoogle Scholar[3] P. Lax and , R. S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York, 1967xii+276 pp. (1 plate) 36:530 0186.16301 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 27, Issue 2| 1985SIAM Review History Published online:02 August 2006 InformationCopyright © 1985 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1027082Article page range:pp. 274-275ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

DOI: 10.1137/1027082

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Previous article Next article Scattering Theory by the Enss Method (Peter A. Perry) (B. Simon, ed.)George A. HagedornGeorge A. Hagedornhttps://doi.org/10.1137/1027082PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Scattering Theory by the Enss Method (Peter A. Perry) (B. Simon, ed.)." SIAM Review, 27(2), pp. 274–275[1] Volker Enss, Asymptotic completeness for quantum mechanical potential scattering. I. Short range potentials, Comm. Math. Phys., 61 (1978), 285–291 58:25583 0389.47005 CrossrefISIGoogle Scholar[2] Volker Enss, P. Blanchard, Completeness of three-body quantum scatteringDynamics and processes (Bielefeld, 1981), Lecture Notes in Math., Vol. 1031, Springer, Berlin, 1983, 62–88, Heidelberg–New York 85h:81071 0531.47009 CrossrefGoogle Scholar[3] P. Lax and , R. S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York, 1967xii+276 pp. (1 plate) 36:530 0186.16301 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 27, Issue 2| 1985SIAM Review History Published online:02 August 2006 InformationCopyright © 1985 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1027082Article page range:pp. 274-275ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

In this lecture we give more details of an alternative approach to quantum scattering theory, initiated by V. Enss, This approach is based on a geometric analysis of the behavior for

t \rightarrow \pm \infty

of the solutions of Schroedinger’s equation for initial data in the subspace of absolute continuity for the hamiltonian H . 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.

Previous article Next article Variational Problem for Overlapping Laser Pulses (C. E. Carroll)David AllwrightDavid Allwrighthttps://doi.org/10.1137/1034060PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] C. E. Carroll, Minimum area for complete inversion of a three-state atom, Phys. Rev., A 39 (1989), 2243–2244 10.1103/PhysRevA.39.2243 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails From Snell’s law to Fermat’s principleJournal of Sound and Vibration, Vol. 536 | 1 Oct 2022 Cross Ref Volume 34, Issue 2| 1992SIAM Review History Published online:02 August 2006 InformationCopyright © 1992 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1034060Article page range:pp. 310-312ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

^{1}

G. Placzek, Handbuch der Radiologie, ed. by E. Marx (Academische Verlag., Leipzig, 1934) Vol. VI, Part 2, pp. 205.

^{2}

C. H. Ting, the following paper.

^{3}

H A. Kramers and W.C. Heisenberg, Z. Physik 31, 681 (1925).

Previous article Next article Solvable Models in Quantum Mechanics (S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, and H. Holden)F. H. BrownellF. H. Brownellhttps://doi.org/10.1137/1032018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. Weyl, Ramifications, old and new, of the eigenvalue problem, Bull. Amer. Math. Soc., 56 (1950), 115–139 11,666i 0041.21003 CrossrefISIGoogle Scholar[2] F. H. Brownell, Spectrum of the static potential Schrödinger equation over $E\sb n$, Ann. of Math. (2), 54 (1951), 554–594 13,847a 0044.42703 CrossrefISIGoogle Scholar[3] F. A. Berezin and , L. D. Faddeev, A remark on Schrödinger's equation with a singular potential, Soviet Math. Dokl., 2 (1961), 372–375 0117.06601 Google Scholar[4] C. N. Friedman, Perturbations of the Schröedinger equation by potentials with small support, J. Functional Analysis, 10 (1972), 346–360 10.1016/0022-1236(72)90033-X 49:5529 0235.35009 CrossrefGoogle Scholar[5] F. H. Brownell, Real variables and Hilbert space operators for scientists, University Microfilms International, Ann Arbor, MI, 1978 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the relation between two different methods to treat Hamiltonians with point interactionsIntegral Equations and Operator Theory, Vol. 14, No. 3 Cross Ref Volume 32, Issue 1| 1990SIAM Review History Published online:18 July 2006 InformationCopyright © 1990 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1032018Article page range:pp. 160-167ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Quantum Mechanics in Hilbert Space (Eduard Prugovecki)J. M. CookJ. M. Cookhttps://doi.org/10.1137/1015056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Quantum Mechanics in Hilbert Space (Eduard Prugovecki)." SIAM Review, 15(2), pp. 403–404 Previous article Next article FiguresRelatedReferencesCited byDetails Volume 15, Issue 2| 1973SIAM Review History Published online:02 August 2006 InformationCopyright © 1973 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1015056Article page range:pp. 403-404ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics