On a perturbation of a class of Schr"odinger systems in $L^2$-spaces

Abstract

The aim of this short note is to prove a generation result of $C_0$-semigroups in $L^2(\Rd, \Cm)$, with the characterization of the domain of their generators, for a perturbation of a class of matrix Schr"odinger operators by symmetric potential matrices whose entries can grow exponentially at infinity. A further perturbation by drift matrices with entries that can grow at most linearly at infinity, is considered. Finally, suitable assumptions which guarantee that the generated semigroups are analytic, are provided too.