  Two problems incorporating a set of horizontal linear potentials crossed by a
sloped linear potential are analytically solved and compared with numerical
results: (a) the case where boundary conditions are specified at the ends of a
finite interval, and (b) the case where the sloped linear potential is replaced
by a piecewise-linear sloped potential and the boundary conditions are
specified at infinity. In the approximation of small gaps between the
horizontal potentials, an approach similar to the one used for the degenerate
problem (Yurovsky V A and Ben-Reuven A 1998 J. Phys. B 31,1) is applicable for
both problems. The resulting scattering matrix has a form different from the
semiclassical result obtained by taking the product of Landau-Zener amplitudes.
Counterintuitive transitions involving a pair of successive crossings, in which
the second crossing precedes the first one along the direction of motion, are
allowed in both models considered here.
