Geodesic
Time dependent delta-prime interactions in dimension one
Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 2, pp. 303-314.

Voir la notice de l'article provenant de la source Math-Net.Ru

We solve the Cauchy problem for the Schrödinger equation corresponding to the family of Hamiltonians $H_{\gamma(t)}$ in $L^2(\mathbb{R})$ which describes a $\delta'$-interaction with time-dependent strength $1/{\gamma(t)}$. We prove that the strong solution of such a Cauchy problem exists whenever the map $t\mapsto\gamma(t)$ belongs to the fractional Sobolev space $H^{3/4}(\mathbb{R})$, 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.
Keywords: time dependent point interactions, delta-prime interaction, non-autonomous Hamiltonians. 
@article{NANO_2016_7_2_a2,
     author = {C. Cacciapuoti and A. Mantile and A. Posilicano},
     title = {Time dependent delta-prime interactions in dimension one},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {303--314},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2016_7_2_a2/}
}
TY  - JOUR
AU  - C. Cacciapuoti
AU  - A. Mantile
AU  - A. Posilicano
TI  - Time dependent delta-prime interactions in dimension one
JO  - Nanosistemy: fizika, himiâ, matematika
PY  - 2016
SP  - 303
EP  - 314
VL  - 7
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/NANO_2016_7_2_a2/
LA  - en
ID  - NANO_2016_7_2_a2
ER  - 
%0 Journal Article
%A C. Cacciapuoti
%A A. Mantile
%A A. Posilicano
%T Time dependent delta-prime interactions in dimension one
%J Nanosistemy: fizika, himiâ, matematika
%D 2016
%P 303-314
%V 7
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/NANO_2016_7_2_a2/
%G en
%F NANO_2016_7_2_a2
C. Cacciapuoti; A. Mantile; A. Posilicano. Time dependent delta-prime interactions in dimension one. Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 2, pp. 303-314. http://geodesic.mathdoc.fr/item/NANO_2016_7_2_a2/