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).