Semiclassical approximation and 1/n expansion in quantum-mechanical problems

The semiclassical approximation and the technique of 1/n expansion are used to calculate the eigenenergies and the wave functions for the radial Schrodinger equation. It is shown that the expressions that are asymptotically exact in the limit n = n(r) + l + 1 --> infinity and which describe the above eigenenergies and the asymptotic coefficients at the origin and at infinity ensure a satisfactory precision even for states characterized by modest values of the quantum numbers II, and I, including the ground state. (C) 2001 MAIK "Nauka/Interperiodica".