Expansion and one-range addition theorems for complete orthonormal sets of spinor wave functions and Slater spinor orbitals of arbitrary half-integral spin in position, momentum and four-dimensional spaces

TL;DR

This paper develops analytical expansion and addition theorems for relativistic spinor wave functions and Slater spinor orbitals of arbitrary half-integer spin across multiple spaces, facilitating complex integral calculations in advanced quantum theories.

Contribution

It introduces new relativistic expansion and addition theorems for spinor functions expressed via nonrelativistic counterparts, applicable in various spaces.

Findings

Derived theorems for position, momentum, and four-dimensional spaces.

Expressed relativistic theorems through nonrelativistic spin-0 theorems.

Facilitates computation of multicenter integrals in relativistic quantum chemistry.

Abstract

The analytical relations in position, momentum and four-dimensional spaces are established for the expansion and one-range addition theorems of relativistic complete orthonormal sets of exponential type spinor wave functions and Slater spinor orbitals of arbitrary half-integral spin. These theorems are expressed through the corresponding nonrelativistic expansion and one-range addition theorems of the spin-0 particles introduced by the author. The expansion and one-range addition theorems derived are especially useful for the computation of multicenter integrals over exponential type spinor orbitals arising in the generalized relativistic Dirac-Hartree-Fock-Roothaan theory when the position, momentum and four-dimensional spaces are employed.