Geodesic
Time dependent delta-prime interactions in dimension one
Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 2, pp. 303-314 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {C. Cacciapuoti and A. Mantile and A. Posilicano},
     title = {Time dependent delta-prime interactions in dimension one},
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     year = {2016},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2016_7_2_a2/}
}
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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/