New approach to the solution of the scattering of spinless particles by central potentials

The explicit forms of the regular solutions, of the Jost solutions and functions for the radial Schrödinger equation, which describe the scattering of spinless particles by central potentials, are found. The regular solutions are derived from the iterative solution of the integral equation which their suitably modified Laplace transforms fulfil. Two general classes of potentials are used each of them being expressed by the corresponding inverse Laplace transform. As such forms of the regular solutions are related to those of the Jost solutions, the Jost solutions (along with the Jost functions) are written directly. The regions of the complex angular momenta and wave numbers, to which they can be analytically continued, are specified. Some testing relations are also derived.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.