Unified treatment of complete orthonormal sets of functions in coordinate, momentum and four-dimensional spaces and their expansion and one-range addition theorems

Abstract

The simpler formulas are derived for the complete orthonormal sets of exponential- type orbitals, momentum space orbitals and hyperspherical harmonics and their expansion and one-range addition theorems. The continuum states are not properly included in these functions. The analytical formulas are also obtained for the overlap integrals over Ψα-ETOs, their extensions to momentum and four-dimensional spaces and STOs with the same screening constants using addition and expansion theorems derived in this paper. The complete orthonormal sets of functions and their expansion and one-range addition theorems obtained can be useful in the study of different quantum mechanical problems when the coordinate, momentum or four-dimensional spaces employed.