najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-2-303-314najo-829Research ArticleINVITED SPEAKERSINVITED SPEAKERSTime dependent delta-prime interactions in dimension oneTime dependent delta-prime interactions in dimension oneCacciapuotiC.CacciapuotiC.

via Valleggio 11, 22100 Como

via Valleggio 11, 22100 Como

claudio.cacciapuoti@uninsubria.itMantileA.MantileA.

Moulin de la Housse BP 1039, 51687 Reims

Moulin de la Housse BP 1039, 51687 Reims

andrea.mantile@univ-reims.frPosilicanoA.PosilicanoA.

via Valleggio 11, 22100 Como

via Valleggio 11, 22100 Como

DiSAT, Sezione di Matematica, Universit`a dell’InsubriaDiSAT, Sezione di Matematica, Universit`a dell’InsubriaLaboratoire de Math´ematiques, Universit´e de ReimsLaboratoire de Math´ematiques, Universit´e de Reims20161308202572Special Issue303314Copyright © Cacciapuoti C., Mantile A., Posilicano A., 20252025Cacciapuoti C., Mantile A., Posilicano A.Cacciapuoti C., Mantile A., Posilicano A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/829

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.

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.

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The authors declare that there are no conflicts of interest present.