#### Filter Results:

#### Publication Year

1981

2015

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

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)

- Claudy Cancelier, André Martinez, Thierry, Ramond
- 2004

— 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)

- Vincenzo Grecchi, Marco Maioli, André Martinez
- 2009

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)

- André Martinez, Shu Nakamura, Vania Sordoni
- 2004

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)

- ‹
- 1
- ›