Verallgemeinerte Summationsprozesse als numerische Hilfsmittel f\"ur quantenmechanische und quantenchemische Rechnungen

Abstract

Slowly convergent or divergent sequences and series occur abundantly in quantum physics and quantum chemistry. These convergence problems can be overcome with the help of nonlinear sequence transformations (Wynn's epsilon or rho algorithm, Brezinski's theta algorithm, Levin's transformation, etc.) as for instance described in E. J. Weniger, "Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series", Comput. Phys. Rep. Vol. 10, 189 - 371 (1989). A detailed description of the mathematical properties of these transformations is given. The nonlinear sequence transformations are applied for the evaluation of special or auxiliary functions by summing divergent asymptotic expansions via rational approximants, for the evaluation of complicated molecular multicenter integrals, for the summation of the divergent perturbation expansions of the anharmonic oscillators, or for the extrapolation of quantum chemical cluster calculations on stereoregular quasi-one-dimensional polymers to the infinite chain limit.