Abstract
A numerical method of the partial coordinate splitting for solving the 3+1 dimensional Schrödinger equation is proposed. The method is applied to the calculation of the multi-fold differential cross section of the ionization of the hydrogen atom and the hydrogen molecular ion by a fast electron impact. We propose a direct approach, which involves the reduction of the initial 6D Schrodinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics, thus avoiding the use of functions of the continuous spectrum of the ejected electron. The results obtained, after verification of the procedure in the case of atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.