Two new solvable potentials

We succeeded in finding two new solvable potentials by working in a complete square integrable basis that carries a tridiagonal (Jacobi) matrix representation for the wave operator. The conventional methods do not lead to exact solutions for these potentials. Hence, a new approach has been adopted for these potentials. First, we obtain the potential parameter spectrum (the set of values of the potential parameters that lead to an exact solution at a given energy). Then, the map that associates the parameter spectrum with the energy is inverted to give the energy spectrum for a given potential parameter. This procedure has been applied in 3D to obtain the energy spectrum for a special screened Coulomb potential with a barrier and in 1D for a single wave potential.