On a perturbation of a class of Schroedinger systems in L^2 spaces

The aim of this short note is to prove a generation result of $C_0$-semigroups in $L^2(Rd, Cm)$, with a characterization of the domain of the generator, for a perturbation of a class of matrix Schr"odinger operators by symmetric potential matrices whose entries can grow exponentially. 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 semigroup generated is analytic are provided too.