Seminar

The thesis developed an algorithmic approach to the construction of schemes of the finite element method of high accuracy and the Kantorovich method - reduction to a system of ordinary differential equations for solving multidimensional boundary-value problems for Schrodinger equation and investigation the quantum system of several particles. The operability of the constructed computing schemes, the created numerical and symbolic computer-algebraic algorithms and problem-oriented complexes of programs realizing them is confirmed by a numerical analysis of exact solvable and reference tasks with the known solutions and also physically interesting configurations and resonant processes possible in the quantum systems of several particles: photo-absorbtion in ensembles of the axial and symmetric quantum dotes, a Coulomb scattering of an electron in the homogeneous magnetic field and a photo-ionization of atom of Hydrogen, scattering of a diatomic molecule on atom or a potential barrier, tunneling of an cluster from several identical quantum particles through potential barriers or wells.