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Reeh–Schlieder-type density results in one- and n-body Schrödinger theory and the "unique continuation problem"

Requardt, Manfred (1986) Reeh–Schlieder-type density results in one- and n-body Schrödinger theory and the "unique continuation problem". Journal of Mathematical Physics, 27 (6). pp. 1571-1577. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:REQjmp86

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Abstract

A couple of Reeh–Schlieder-type density results are proved to hold in one- and n-body Schrödinger theory, that is, it is proved that states localized at time zero in an arbitrarily small open set of Rn are already total after an arbitrarily small time (which implies much more than the well-known acausal behavior of nonrelativistic theories). It is shown that there exists a close connection to the so-called "unique continuation property" of elliptic partial differential operators. Furthermore, a certain machinery of analytic continuation is developed and the notion of generalized propagation kernels is introduced, which also might be of use elsewhere (e.g., in scattering theory).


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.527068DOIUNSPECIFIED
http://link.aip.org/link/?JMAPAQ/27/1571/1PublisherUNSPECIFIED
Additional Information:Copyright © 1986 American Institute of Physics. Received 1 August 1985; accepted 8 January 1986. This paper was written while I was a guest at the California Institute of Technology. I would like to thank Professor W. A. Luxemburg and Professor B. Simon for their kind hospitality. I would also like to thank the Deutsche Forschungsgemeinschaft for financial support.
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Subject Keywords:QUANTUM OPERATORS, KERNELS, PARTIAL DIFFERENTIAL EQUATIONS, FUNCTIONAL ANALYSIS, ANALYTIC FUNCTIONS, QUANTUM MECHANICS, POTENTIALS
Record Number:CaltechAUTHORS:REQjmp86
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:REQjmp86
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12026
Collection:CaltechAUTHORS
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Deposited On:20 Oct 2008 18:25
Last Modified:26 Dec 2012 10:25

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