We present a grid method to solve the time dependent Schro Β¨dinger equation (TDSE). It uses the Crank-Nicholson scheme to propthen solving the resulting eigenproblem by expanding on agate the wavefunction forward in time and finite differences to some basis set. Examples of such techniques are the colloapproximate the derivative operators. The resulting sparse linear cation and Galerkin methods implemented via piecewise system is solved by the symmetric successive overrelaxation iterapolynomials such as the cubic [3] or quintic Hermite [7] tive technique. The method handles local and nonlocal interactions and Hamiltonians that correspond to either Hermitian or to non-splines, and the B-splines [4,8]. These methods are nowa-Hermitian matrices with real eigenvalues. We test the method by days extensively used in the field of few-body systems. solving the TDSE in the imaginary time domain, thus converting the Expansions in terms of general basis sets are also employed time propagation to asymptotic relaxation. Benchmark problems in the configuration interaction method [9], in the Hartreesolved are both in one and two dimensions, with local, nonlocal, Fock method [10], in variational methods [11], etc. The Hermitian and non-Hermitian Hamiltonians.