A Study of the Lippmann-Schwinger Equation and Spectra for Some Unbounded Quantum Potentials

Christopher J. Winfield

Type: Article

Publication Date: 2005-08-01

Citations: 1

DOI: https://doi.org/10.1216/rmjm/1181069691

Abstract

In this article we study the Modified Lippmann Schwinger equation for certain model potentials V defined on R 3 , not of Rollnik class, and solutions to the equation in a weak sense.Further, we study the resolvent and the spectrum of the operator H = -Δ + cV in our model for nonzero constants c.In particular, we find that, for sufficiently small c > 0, H has no singular spectrum.

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Rocky Mountain Journal of Mathematics - View - PDF

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+	Spectral Theory of Operators in Hilbert Space	1973	Kurt Friedrichs
+ PDF Chat	Hamiltonians defined as quadratic forms	1971	Barry Simon
+ PDF Chat	On the essential spectrum of the hydrogen energy and related operators	1966	Peter Rejto
+	Singular Integrals and Differentiability Properties of Functions (PMS-30)	1971	Elias M. Stein
+	Schrödinger Scattering Amplitude. III	1962	A. Großmann Tai Tsun Wu
+	Theory of Simple Scattering and Eigenfunction Expansions	1970	Tosio Kato S. T. Kuroda