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Distortion analyticity and molecular resonance curves. (English) Zbl 0619.46068

Resonance energies of n electrons in the field of N fixed nuclei are defined as discrete eigenvalues of non-selfadjoint operators which arise from the Hamiltonian H by a general class of complex distortions of \({\mathbb{R}}^ 3\) around the fixed nuclei. They are identified with the poles in the analytic continuation of resolvent matrix-elements \((\phi,(z-H)^{-1}\psi)\) between states \(\phi\), \(\psi\) of an explicitely given set A of analytic vectors, and thus shown to be independent of the particular choice of the distortion. Distortions are also used to derive local analyticity properties of bound state- and resonance energies in the nuclear coordinates.
The same techniques also yield existence and uniqueness of solutions to the Schrödinger equation for n electrons in the time-dependent field of classically moving (non-colliding) nuclei.

MSC:

46N99 Miscellaneous applications of functional analysis
81V10 Electromagnetic interaction; quantum electrodynamics
47F05 General theory of partial differential operators
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