A NEW 1/N-EXPANSION PROCEDURE

An effective method is developed for calculating the 1/N-expansion coefficients of arbitrary high orders both for the ground and radially excited states of the discrete spectrum of the Schrodinger equation. The method is based on the semiclassical interpretation of the 1/N-expansion. The explicit application of the expansion over the Planck's constant clarifies the cause of the complementarity in the 1/N-approach and WKB approximation. The transition to the Riccati equation and h-expansion allows to apply the quantization condition for involving thte wavefunction nodes, what results in the simple recursive relations. In the example of the funnel - shaped potential the calculations are given for the first ten coefficients in the 1/n-expansion scheme for energy with the various values of the orbital and radial quantum numbers.