Mathematical Physics, Analysis and Geometry

, Volume 13, Issue 1, pp 83–103 | Cite as

Time-dependent Delta-interactions for 1D Schrödinger Hamiltonians



The non autonomous Cauchy problem \(i\partial_{t}u=-\partial_{xx}^{2} u+\alpha(t) \delta_{0}u\) with u t = 0 = u 0 is considered in L 2 (ℝ) . The regularity assumptions for α 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.


Point interactions Solvable models in Quantum Mechanics Non-autonomous Cauchy problems 

Mathematics Subject Classifications (2000)

37B55 35B65 35B30 35Q45 


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.IRMAR, UMR-CNRS 6625Université Rennes 1Rennes CedexFrance

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