Time-dependent delta-interactions for 1D Schrödinger Hamiltonians

Details Time-dependent delta-interactions for 1D Schrödinger Hamiltonians Time-dependent delta-interactions for 1D Schrödinger Hamiltonians

2009-03-31

arxiv.org/abs/0903.5452v1

Physics

Mathematical Physics

Scientific paper

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.

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