André Martinez

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We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case where the electronic Hamiltonian admits a local gap in its spectrum. In particular, we show that the molecular(More)
— We propose a definition for the resonances of Schrödinger operators with slowly decaying C ∞ potentials without any analyticity assumption. Our definition is based on almost analytic extensions for these potentials, and we describe a systematic way to build such an extension that coincide with the function itself whenever it is analytic. That way, if the(More)
We prove the Padé (Stieltjes) summability of the perturbation series of the energy levels of the cubic anharmonic oscillator, H 1 (β) = p 2 + x 2 + i p βx 3 , as suggested by the numerical studies of Bender and Weniger. At the same time, we give a simple and independent proof of the positivity of the eigenvalues of the PT-symmetric operator H 1 (β) for real(More)
We study microlocal analytic singularity of solutions to Schrödinger equation with analytic coefficients. Using microlocal weight estimate developped for estimating the phase space tunneling, we prove microlo-cal smoothing estimates that generalize results by L. Robbiano and C. Zuily. We suppose the Schrödinger operator is a long-range type perturbation of(More)
Here we consider one of the basic models for many-body problems under an external field: the molecule ion H + 2 under the effect of an external Stark-type potential. If we consider the vibrational energy levels of the first two electronic states of the molecule ion H + 2 then, in the semiclassical limit and by means of a suitable modified Born-Oppenheimer(More)
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