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Schrödinger operators at threshold. (English) Zbl 0787.35056

Albeverio, Sergio (ed.) et al., Ideas and methods in quantum and statistical physics. In memory of Raphael Hœgh-Krohn (1938-1988). Volume 2. Cambridge: Cambridge University Press. 173-196 (1992).
Summary: Recent results are reviewed on the zero-energy threshold scattering for Schrödinger operators in \(d \leq 3\) dimensions. The possibility of zero- energy resonances and/or zero-energy bound states of the Hamiltonian is taken into account explicitly. No spherical symmetry of the interaction is assumed. In particular, Laurent expansions around threshold are provided for the transition operator, the scattering amplitude, the scattering operator and the trace of the resolvent difference. Low energy parameters like e.g. the scattering length are defined and related directly to the threshold behavior of the scattering amplitude. Spectral sum rules, in particular Levinson’s theorem, are discussed.
For the entire collection see [Zbl 0747.00053].

MSC:

35P25 Scattering theory for PDEs
35Q40 PDEs in connection with quantum mechanics
81U05 \(2\)-body potential quantum scattering theory

Citations:

Zbl 0747.00053
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