Feshbach reduction scheme for general Hamiltonians in the Born-Oppenheimer approximation
• abderrahmane senoussaoui,
• Tayeb Taifour
abderrahmane senoussaoui
University of Oran 1
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Tayeb Taifour
University of Oran
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## Abstract

We study the spectral properties of resonances of general Hamiltonians in the Born-Oppenheimer approximation. We prove that this study can be reduced to the one of a family of finite matrices of semiclassical $$h$$-pseudodifferential operators. More precisely, we show that any resonance which is close enough to the real axis can be obtained from the discrete spectrum of one of these matrixes.