2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140898We study the S-matrix for the transitions at an avoided crossing of several energy levels, which is a multilevel generalization of the Landau-Zener problem. We demonstrate that, by extending the Schroedinger evolution to complex time, one can obtain an exact answer for some of the transition amplitudes. Similar to the Landau-Zener case, our result covers both the adiabatic regime (slow evolution.) and the diabatic regime (fast evolution). The form of the exact transition amplitude coincides with that obtained in a sequential pairwise level crossing approximation, in accord with the conjecture of Brundobler and Elser.3 pages, 2 figuresMesoscale and Nanoscale PhysicsQuantum Physicstext