Higher orders of perturbation theory, classical mechanics and the 1/n expansion

As is known, in quantum mechanics and field theory higher orders of perturbation theory (PT) are increasing with the PT order k as a factorial of k. The results of calculations of PT higher orders and summation methods of diverging PT series for a wide class of quantum-mechanical problems (including Yukawa and Hulthen potentials, the V-funnel potential etc.) are discussed. It is shown that along this line one can obtain a highly accurate value of the level energy (for stationary, virtual and quasi-stationary levels), basing upon the PT coefficients. The energy asymptotics for highly excited states is obtained by transition to classical mechanics, and quantum corrections to the energy are evaluated. The calculations confirm the results obtained by summation of the PT series