Hydrogenic orbitals in Momentum space and hyperspherical harmonics: Elliptic Sturmian basis sets

摘要: Momentum space hydrogenic orbitals can be regarded as orthonormal and complete Sturmian basis sets explicitly given in terms of (hyper)-spherical harmonics on the 4-D hypersphere S 3 . Among alternative coordinate systems that allow separation variables, usual ones involving parameterizations sphere by circular functions correspond to canonical subgroup reduction chains; we also investigate harmonic "elliptic" (as, e.g., obtained Jacobi elliptic functions). In this article list orthogonal transformations connecting them. The latter enjoy useful three-term recurrence relationships their efficient calculations even for large strings. We consider modifications needed when conservation symmetry Sturmians with respect parity. Finally, discuss some properties relations Sturmians. Because cannot expressed closed form, it is important find expansions a suitable set calculate transformation coefficients. derive recursion fulfilled coefficients between A concluding discussion connections configuration momentum completes article. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 92: 212-228,