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Published June 1986 | Published
Journal Article Open

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

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).

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.

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August 22, 2023
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