  In this paper we study some particular types of matrix Schr\"odinger
semigroups of the form $\exp(-it\mathbb{H})$ where $\mathbb{H}\in
M_N(\mathbf{C})$ is the Hamiltonian of a given quantum dynamical system modeled
in the finite dimensional Hilbert space $\mathcal{H}$. Once we have defined a
particular matrix Schr\"odinger unitary group we perform some estimates for its
approximation and its corresponding implementation in the numerical solution of
the finite dimensional Schr\"odinger evolution equation to that it is related.
