Exact analytical solution of time-independent Schrodinger equation for a system consisting of two flat potentials coupled by a rectangular potential

We have proposed an analytical method for finding the exact solution for the two-state scattering problems, where two flat potentials are coupled by a rectangular potential. We found a way to express the two-state problem by an effective single-state problem, where it is easy to estimate the transition probability from one potential to the other by estimating the amount of missing flux from the first potential. This has been an unsolved problem for a long time and is of considerable importance as a model for non-adiabatic electronic transition.