Hydrogenic orbitals in momentum space and hyperspherical harmonics. Elliptic sturmian basis sets.

In this article we list the canonical hydrogenic Sturmian sets and the orthogonal transformations connecting them. The latter enjoy useful three-term recurrence relationships that allow their coefficient calculations even for large strings. The properties of elliptic hydrogenic Sturmians and their relations with canonical Sturmians are investigated. We derive three-term recursion relationships fulfilled by the coefficients of the transformation between elliptic Sturmians and canonical Sturmians. A discussion on the connections between configuration space and momentum space representations completes this article.