The d-dimensional hydrogen atom: hyperspherical harmonics as momentum space orbitals and alternative Sturmians basis sets

Sturmian basis sets in configuration space - corresponding to variable separation in parabolic coordinates - are introduced as alternatives to the ordinary ones in spherical coordinates. Extensions of Fock stereographic projections allow us to establish the relationships between the corresponding momentum space orbitals and the alternative forms of hyperspherical harmonics. 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 generalized vector coupling coefficients. The use of these orbitals as complete and orthonormal expansion basis sets for atomic and molecular problems is briefly discussed.