Time dependent delta-prime interactions in dimension one
https://doi.org/10.17586/2220-8054-2016-7-2-303-314
Abstract
We solve the Cauchy problem for the Schrӧdinger equation corresponding to the family of Hamiltonians Hγ(t) in L2(R) which describes a δ′-interaction with time-dependent strength 1/γ(t). We prove that the strong solution of such a Cauchy problem exists whenever the map t → γ(t) belongs to the fractional Sobolev space H3/4(R), thus weakening the hypotheses which would be required by the known general abstract results. The solution is expressed in terms of the free evolution and the solution of a Volterra integral equation.
Supporting agencies: The authors acknowledge the support of the FIR 2013 project “Condensed Matter in Mathematical Physics”, Ministry of University and Research of Italian Republic (code RBFR13WAET).
About the Authors
C. Cacciapuoti
DiSAT, Sezione di Matematica, Universit`a dell’Insubria
Italy
Italy
via Valleggio 11, 22100 Como
A. Mantile
Laboratoire de Math´ematiques, Universit´e de Reims
France
France
Moulin de la Housse BP 1039, 51687 Reims
A. Posilicano
DiSAT, Sezione di Matematica, Universit`a dell’Insubria
Italy
Italy
via Valleggio 11, 22100 Como
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Review
For citations:
Cacciapuoti C., Mantile A., Posilicano A. Time dependent delta-prime interactions in dimension one. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(2):303-314. https://doi.org/10.17586/2220-8054-2016-7-2-303-314
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