A modification of the Bohr-Sommerfeld quantization condition

The Bohr-Sommerfeld quasiclassical quantization condition for a central potential is modified in such a way that the constant γ becomes dependent on the angular momentum l and on the potential behaviour at small distances. This form of the quantization condition is especially simple in the case l = 0. When applied to some particular potentials, taken as examples, the present approximation provides more accurate values of the level energies than the conventional form of quantization condition. Application of the quasiclassical approach to singular potentials with 'collapse' and to the superstrong Coulomb Field induced by a charge Z > 137 is also considered. (author)