Wave functions of the Hydrogen atom in the momentum representation

We construct the integral transform passing from the space representation to the radial momentum representation for the Hydrogen atom. The resulting wave functions are explicitly given in terms of complex finite expansions of Gegenbauer functions of the first and second kind, or in terms of (elementary) trigonometric functions. We show their symmetry under the SO(4) group, and their equivalence with those of Lombardi and Ogilvie

Automated summary

This paper presents the construction of an integral transform that converts the representation of the Hydrogen atom from space to radial momentum. The resulting wave functions are expressed explicitly using complex finite expansions of Gegenbauer functions or (elementary) trigonometric functions. The authors demonstrate the symmetry of these wave functions under the SO(4) group and establish their equivalence to the findings of Lombardi and Ogilvie.