Solutions of the scattering problem in a complete set of Bessel functions with a discrete index

Abstract

We use the tridiagonal representation approach to solve the radial Schrödinger equation for the continuum scattering states of the Kratzer potential. We do the same for a radial power-law potential with inverse-square and inverse-cube singularities. These solutions are written as infinite convergent series of Bessel functions with a discrete index. As physical application of the latter solution, we treat electron scattering off a neutral molecule with electric dipole and electric quadrupole moments.

References in corpus (2)

• Analytic solution of the Schrodinger equation for an electron in the field of a molecule with an electric dipole moment
• Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions