A new variational method is devised for obtaining the "best" parameters for trial wave functions of a given type for insertion into the integral equation [see Eq. (1.4a)] for the scattering of scalar plane waves by obstacles with spherical and cylindrical symmetry.The variational procedure is applied to the determination, in the least square sense, of the square well potential which most closely approximates the potential under consideration for a given propagation constant (k₀=2π/λ₀) of the incident wave. We then use as a trial function in the scattering integral equation the sphere (or cylinder) wave function (with the "best" parameters) which was derived in the first two papers of this series.The differential and total scattering cross sections for scattering by Gaussian, exponential, and screened Coulomb potentials are obtained in simple closed forms. The Born approximation predicts the ratio of the total scattering cross section to πb² (where b is

+More

trial wave functions born approximation variational procedure scattering integral equation potential best parameters gaussian exponential and screened coulomb potentials of the incident wave sphere or cylinder wave function determination differential and total scattering cross scattering of scalar plane waves obstacles propagation constant spherical and cylindrical least square sense of the square well potential bsup2sup where b

Elliott W. Montroll J. Mayo Greenberg,.Scattering of Plane Waves by Soft Obstacles. III. Scattering by Obstacles with Spherical and Circular Cylindrical Symmetry. 86 (6),889–898.

Elliott W. Montroll J. Mayo Greenberg,"Scattering of Plane Waves by Soft Obstacles. III. Scattering by Obstacles with Spherical and Circular Cylindrical Symmetry" 86

Elliott W. Montroll J. Mayo Greenberg,"Scattering of Plane Waves by Soft Obstacles. III. Scattering by Obstacles with Spherical and Circular Cylindrical Symmetry"