Higher Orders of the Perturbation Theory and Summation of Perturbational Series in Quantum Mechanics

摘要

Calculation of higher orders of the perturbation theory is considered for screened Coulomb potentials. Particular cases of such potentials are the Yukawa potential, a familiar object of nuclear physics, and the funnel-shaped potential, applied to analysis of heavy quark-antiquark systems. The calculation of higher perturbational orders is reduced to recursive relations, quite appropriate for computer. The Pade approximants and a modified Pade-Borel summation method are applied for calculation of sums of diverging PT series. It is shown that in the considered problems higher orders of the PT determine the behaviour of E(g) in the region of strong coupling (Esub(g)-the energy of eigen-value). (Atomindex citation 14:751920)