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Zbl 0619.46068
Hunziker, W.
Distortion analyticity and molecular resonance curves. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 45, 339-358 (1986). ISSN 0246-0211

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 ${\bbfR}\sp 3$ around the fixed nuclei. They are identified with the poles in the analytic continuation of resolvent matrix-elements $(\phi,(z-H)\sp{-1}\psi)$ 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. \par 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 2000:: *46N99 Appl. of functional analysis
81V10 Electromagnetic interaction
47F05 Partial differential operators

Keywords: Resonance energies; discrete eigenvalues of non-selfadjoint operators; complex distortions; bound state; resonance; existence and uniqueness of solutions to the Schrödinger equation for n electrons in the time- dependent field of classically moving (non-colliding) nuclei

Cited in: Zbl 1197.35087

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