标题： 一维中的时间依赖的delta-prime相互作用 显示英文标题

标题： Time dependent delta-prime interactions in dimension one

摘要： 我们求解对应于描述$\delta'$与时间依赖强度$1/\gamma(t)$相互作用的哈密顿量族$H_{\gamma(t)}$在$L^{2}(\mathbb{R})$中的薛定谔方程的柯西问题。 我们证明，当映射$t\mapsto\gamma(t)$属于分数索伯列夫空间$H^{3/4}(\mathbb{R})$时，这样的柯西问题的强解存在，从而弱化了已知的一般抽象结果所要求的假设。 该解用自由演化和一个伏尔泰拉积分方程的解来表示。 显示英文摘要

摘要： We solve the Cauchy problem for the Schr\"odinger equation corresponding to the family of Hamiltonians $H_{\gamma(t)}$ in $L^{2}(\mathbb{R})$ which describes $\delta'$ interactions with time-dependent strength $1/\gamma(t)$. We prove that the strong solution of such a Cauchy problem exits 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.