Nonrelativistic, Quasirelativistic and Relativistic Sets of Wave Functions, and Slater Orbitals of Particles with Arbitrary Spin

TL;DR

This paper develops analytical relations for relativistic tensor wave functions and Slater orbitals of particles with arbitrary spin, expressing them through nonrelativistic and quasirelativistic orbitals, and derives formulas for overlap integrals.

Contribution

It introduces new analytical relations for relativistic tensor wave functions and Slater orbitals based on previously established nonrelativistic and quasirelativistic basis sets.

Findings

Derived analytical relations for relativistic tensor wave functions.

Expressed relativistic functions through nonrelativistic and quasirelativistic orbitals.

Obtained formulas for overlap integrals over relativistic tensor Slater orbitals.

Abstract

Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor wave functions and tensor Slater orbitals in coordinate, momentum and four-dimensional spaces are derived, where. The relativistic tensor function sets are expressed through the corresponding nonrelativistic and quasirelativistic orbitals. The analytical formulas for overlap integrals over relativistic tensor Slater orbitals with the same screening constants in coordinate space are also derived.