Simulation of matter wave scattering on the column of force centers in the semiclassical limit

The new trajectory algorithm for quantum dynamic simulation in the semiclassical limit is introduced. The algorithm is based on the calculation of unique characteristic (“index”) of any given trajectory of correspondent classical problem. This index represents summary information about the critical points which are visited when particle moves along classical trajectory. The diffraction picture is obtained during simulation of quantum diffraction on the flat screen when narrow beam of particles is propagated along the line of force centers with attractive potentials of Gaussian type. It has been shown that there is possibility for focusing of such beams at large distances from the initial scattering center. The explanation of such focusing has been given. This explanation is based on the analysis of quantum dynamics of wave packets in the field of gauss-type potential.