标题： 一维时间相关的delta-prime相互作用 显示英文标题

标题： Time dependent delta-prime interactions in dimension one

摘要： 我们求解了对应于$H_{\gamma(t)}$家族哈密顿量的薛定谔方程的柯西问题，该哈密顿量在$L^{2}(\mathbb{R})$中描述了一个与时间相关的强度$1/\gamma(t)$的$\delta'$相互作用。 我们证明，只要映射$t\mapsto\gamma(t)$属于分数阶索伯列夫空间$H^{3/4}(\mathbb{R})$，此类柯西问题的强解就存在，从而弱化了已知的一般抽象结果所要求的假设条件。 解可以通过自由演化和一个沃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 a $\delta'$-interaction 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.