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 S O (4) group, and their equivalence with those of Lombardi and Ogilvie (2020 Chem. Phys. 538 110886). [ABSTRACT FROM AUTHOR]