Abstract
With the use of a stereographic projection of momentum space into a four-dimensional sphere of unit radius, the possibility of analytical solution of the three-dimensional two-body Lippmann–Schwinger equation with the Coulomb interaction at negative energy has been studied. Simple analytical expressions for the three-dimensional Coulomb transition matrix in the case of the repulsive Coulomb interaction and positive integer values of the Coulomb parameter have been obtained. The worked out method has also been applied to the generalized three-dimensional Coulomb transition matrix in the case of the attractive Coulomb interaction and negative integer values of the Coulomb parameter.
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