On the complex solution of the Schr?dinger equation with exponential potentials

We study the analytical solutions of the Schrodinger equation with a repulsive exponential potential lambda e (-r) , and with an exponential wall lambda e( r) , both with lambda > 0. We show that the complex eigenenergies obtained for the latter tend either to those of the former, or to real rational numbers as lambda -> infinity . In the light of these results, we explain the wrong resonance energies obtained in a previous application of the Riccati-Pade method to the Schrodinger equation with the repulsive exponential potential, and further study the convergence properties of this approach.