Combined theory of complete orthonormal sets of quasirelativistic and relativistic sets of wave functions, and Slater orbitals of spin -1/2 particles in position, momentum and four dimensional spaces

TL;DR

This paper develops complete orthonormal basis sets for spinor wave functions and Slater orbitals in relativistic quantum mechanics, facilitating calculations in position, momentum, and four-dimensional spaces.

Contribution

It introduces new basis sets for quasirelativistic and relativistic spinor wave functions expressed through nonrelativistic orbitals, with analytical formulas for overlap integrals.

Findings

Established basis sets for relativistic spinor wave functions.

Derived analytical formulas for overlap integrals.

Facilitates quantum mechanical calculations in multiple spaces.

Abstract

By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two-and four-component spinor wave functions, and Slater spinor orbitals useful in the quantum-mechanical description of the spin - 1/2 particles by the quasirelativistic and relativistic equations are established in position, momentum and four-dimensional spaces. These function sets are expressed through the corresponding nonrelativistic orbitals. The analytical formulas for overlap integrals over four component relativistic Slater spinor orbitals with the same screening constants in position space are also derived. The relations obtained in this study can be useful in the study of different problems arising in the quasirelativistic and relativistic quantum mechanics when the position, momentum and four dimensional spaces are employed.