Time dependent delta-prime interactions in dimension one

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.