## 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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### References:

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