HYPERSPHERICAL SYMMETRY OF HYDROGENIC ORBITALS AND RECOUPLING COEFFICIENTS AMONG ALTERNATIVE BASES

Fock's representation of momentum space hydrogenic orbitals in terms o f harmonics on the hypersphere S-3 Of a four-dimensional space is exte nded to classify alternative bases. These orbitals are of interest for Sturmian expansions of use in atomic and molecular structure calculat ions and for the description of atoms in fields. Because of the corres pondence between the S-3 manifold and the SU(2) group, new sum rules a re established which are of relevance for the connection, not only amo ng hydrogen atom orbitals in different bases, but also among the usual vector coupling coefficients and rotation matrix elements.