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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 crossingdiabatic potentials with localized initial and localized or delocalized finalstates, in the intermediate energy region, when all four adiabatic states arecoupled and should be taken into account. In fact these situations exhaust allcases practically relevant for spectroscopy of non-rigid molecules (i.e. withmore than one stable configuration).Comment: 19 pages, 8 eps figures, Revtex-4, revised version, one figure is  deleted, and corrected some typos. Accepted to Physical Review

Semiclassical quantization of bound and quasistationary states beyond the adiabatic approximation