EXACT ANALYTICAL SOLUTION FOR COUPLED TIME-INDEPENDENT SCHRODINGER-EQUATIONS WITH CERTAIN MODEL POTENTIALS

An exact analytical solution is obtained for coupled time-independent Schrodinger equations with model potentials: V-11(x) = V-1 + beta V(0) e(-alpha x), V-22(x) = V-2 + 1/beta V(0)e(-alpha x) and V-12(x) = V-21 (x) = V-0 e(-alpha x). This is made possible by solving a single fourt h-order ordinary differential equation derived from the original coupl ed equations. Exact closed-form solutions for the non-adiabatic transi tion matrices (or scattering matrices) are found for scattering bounda ry conditions with three, two and one open channels, respectively. How to apply the present results to deal with general potentials is also briefly analysed.