  In this paper we present a unified picture concerning Lie-Trotter method for
solving a large class of semilinear problems: nonlinear Schr\"odinger,
Schr\"oginger--Poisson, Gross--Pitaevskii, etc. This picture includes more
general schemes such as Strang and Ruth--Yoshida. The convergence result is
presented in suitable Hilbert spaces related with the time regularity of the
solution and is based on Lipschitz estimates for the nonlinearity. In addition,
with extra requirements both on the regularity of the initial datum and on the
nonlinearity we show the linear convergence of the method.
