Semiclassical quantization of bound and quasi-stationary states beyond the adiabatic approximation

19 pages, 8 eps figures, Revtex-4, revised version, one figure is deleted, and corrected some typos.We examine one important (and overlooked in all previous investigations) aspect of well - known crossing diabatic potentials or Landau - Zener (LZ) problem. We derive the semiclassical quantization rules for the crossing diabatic potentials with localized initial and localized or delocalized final states, in the intermediate energy region, when all four adiabatic states are coupled and should be taken into account. In fact these situations exhaust all cases practically relevant for spectroscopy of non-rigid molecules (i.e. with more than one stable configuration)