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Time-dependent Delta-interactions for 1D Schrödinger Hamiltonians

Content Provider	Springer Nature Link
Author	Mantile, Andrea Hmidi, Toufik Nier, Francis
Copyright Year	2009
Abstract	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.
Ending Page	103
Page Count	21
Starting Page	83
File Format	PDF
ISSN	13850172
e-ISSN	15729656
Journal	Mathematical Physics, Analysis and Geometry
Issue Number	1
Volume Number	13
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-12-03
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry Dependence of solutions on initial and boundary data, parameters Smoothness and regularity of solutions Theoretical, Mathematical and Computational Physics Analysis Non-autonomous Cauchy problems Point interactions Solvable models in Quantum Mechanics Group Theory and Generalizations Applications of Mathematics Nonautonomous dynamical systems
Content Type	Text
Resource Type	Article
Subject	Mathematical Physics Geometry and Topology

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Time-dependent delta-interactions for 1d schrödinger hamiltonians. (2009).

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