Time-dependent delta-interactions for 1D Schrödinger Hamiltonians

Taoufik Hmidi (1) , Andrea Mantile (1) , Francis Nier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The non autonomous Cauchy problem for time dependent 1D point interactions is considered. The regularity assumptions for the coupling parameter are accurately analyzed and show that the general results for non autonomous linear evolution equations in Banach spaces are far from being optimal. In the mean time, this article shows an unexpected application of paraproduct techniques, initiated by J.M.~Bony for nonlinear partial differential equations, to a classical linear problem.

Mots clés: Point interactions; solvable models in Quantum Mechanics; non autonomous Cauchy problems

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Taoufik Hmidi, Andrea Mantile, Francis Nier. Time-dependent delta-interactions for 1D Schrödinger Hamiltonians. 2009. ⟨hal-00371803⟩