Analytical solution to the Lippmann–Schwinger equation in the three-dimensional hyperspherical and hyper-pseudospherical spaces
Anderson L. de Jesus, Rafael M. Fortiny, Alexandre G. M. Schmidt
Abstract The present work aims to obtain an exact solution for the Lippmann–Schwinger equation considering a scalar particle in three-dimensional hyperspherical and hyper-pseudospherical spaces. We analytically solve the Lippmann–Schwinger equation for a potential of the boundary-wall type, written as Dirac delta distributions over a two-dimensional single barrier. Our Lippmann–Schwinger equation in space representation is a second-kind Fredholm integral equation, where a bilinear form of the Green’s function leads to a separable kernel. The probability density for the particle, considering level surfaces in both spaces, and the differential cross-section in the hyper-pseudospherical space, are also presented graphically.
Physica Scripta•Jun 17, 2026•0 citations