THE D-DIMENSIONAL HYDROGEN-ATOM - HYPERSPHERICAL HARMONICS AS MOMENTUM-SPACE ORBITALS AND ALTERNATIVE STURMIAN BASIS-SETS

Hydrogenoid orbitals, i.e. the solutions to the Schrodinger equation f or a central Coulomb field, are considered in mathematical dimensions d = 2 and d > 3 different from the physical case, d = 3. Extending kno wn results for d = 3, Sturmian basis sets in configuration (or direct) space - corresponding to variable separation in parabolic coordinates - are introduced as alternatives to the ordinary ones in spherical co ordinates: extensions of Fock stereographic projections allow us to es tablish the relationships between the corresponding momentum (or recip rocal) space orbitals and the alternative forms of hyperspherical harm onics. Properties of the latter and multi-dimensional Fourier integral transforms are exploited to obtain the matrix elements connecting the alternative basis sets explicitly in terms of Wigner's rotation matri x elements for d = 2 and generalized vector coupling (or Hahn) coeffic ients for d > 3. The use of these orbitals as complete and orthonormal expansion basis sets for atomic and molecular problems is briefly com mented.