Analytical solution to the Lippmann-Schwinger equation in the spherical space

The purpose of this work is to obtain an analytical solution to the Lippmann-Schwinger equation for a scalar particle, bounded in a two-dimensional space with constant positive curvature, called the spherical space. Making use of the thin-layer quantization method, we present the free particle wave function solving the Schr & ouml;dinger equation on the spherical space using the Laplace-Beltrami operator. We use the Green's function on the spherical space as the kernel in the Lippmann-Schwinger equation and solve it exactly for the boundary-wall potential, modeled as Dirac delta distributions, considering single, double and finding the generalized result for multiple consecutive barriers. The probability densities are presented graphically.