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 Schroedinger equation. It is shown that the expressions that are asymptotically exact in the limit n = nr + l + 1 → ∞ 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 nr and l, including the ground state