Counterintuitive transitions in multistate curve crossing involving linearpotentials

Two problems incorporating a set of horizontal linear potentials crossed by a sloped linear potential are solved analytically and compared with numeri cal results: (a) the case where boundary conditions are specified at the en ds of a finite interval and (b) the case where the sloped linear potential is replaced by a piecewise-linear sloped potential and the boundary conditi ons are specified at infinity. In the approximation of small gaps between t he horizontal potentials, an approach similar to the one used for the degen erate problem (Yurovsky V A and Ben-Reuven A 1998 J, Phys. B: At. Mel. Opt. Phys. 31 1) is applicable for both problems. The resulting scattering matr ix has a form different from the semiclassical result obtained by taking th e product of Landau-Zener amplitudes. Counterintuitive transitions involvin g a pair of successive crossings, in which the second crossing precedes the first one along the direction of motion, are allowed in both models consid ered here.