Quantum and classical solutions for statically screened two-dimensional Wannier-Mott excitons

Quantum solutions and classical orbits are discussed for statically screened Wannier-Mott excitons for two closely related potentials: the Stern-Howard potential and a suggested simple focusing one. Bound states and exact ''quantized'' values of screening are obtained as well. For the suggested potential, the scattering matrix, the Regge poles, and the transmission coefficient are calculated exactly. We argue that the simple potential can be utilized in applications instead of the Stern-Howard potential, which is difficult to handle.