One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces

The formulae are established in position, momentum, and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine (GCTCP and GETCP HC). These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of ψα-exponential type orbitals (ψα-ETO), φα-momentum space orbitals (φα-MSO), and zα-hyperspherical harmonics (zα-HSH) introduced. The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position, momentum, and four-dimensional spaces are employed. (atomic and molecular physics)