Scattering theory for arbitrary potentials (7 pages)

Stuart C. Althorpe

Wen-Du Li, Wu-Sheng Dai

Abstract In conventional scattering theory, by large-distance asymptotics, at the cost of losing the information of the distance between target and observer, one imposes large-distance asymptotics to achieve a scattering wave function which can be represented explicitly by a scattering phase shift. In this paper, without large-distance asymptotics, we establish an arbitrary-dimensional scattering theory. Arbitrary-dimensional scattering wave functions, scattering boundary conditions, and phase shifts are given without large-distance asymptotics. We give a discussion of one- and two-dimensional scatterings. Moreover, we also suggest a dimensional renormalization scheme to remove the divergence encountered in singular-potential scattering.

George A. Hagedorn

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

Leonard S. Rodberg, Roy M. Thaler, U. Fano