New complete orthonormal sets of exponential type orbitals in standard convention and their origin

TL;DR

This paper introduces new complete orthonormal exponential type orbitals based on spherical harmonics and Laguerre polynomials, linking their origin to self-frictional quantum forces, and discusses their relation to hydrogen-like atom wave functions.

Contribution

The paper presents novel complete orthonormal sets of exponential type orbitals derived from self-frictional quantum forces, expanding the mathematical framework of quantum orbitals.

Findings

New sets of exponential type orbitals are introduced.

Self-frictional quantum forces are identified as their origin.

Orbitals reduce to hydrogen-like wave functions when frictional forces vanish.

Abstract

In standard convention, the new complete orthonrmal sets of exponential type orbitals (ETOs) are introduced as functions of the complex or real spherical harmonics and modified and -generalized Laguerre polynomials (MPLs and GLPs), where, and is the noninteger or integer (for) frictional quantum number. It is shown that the origin of the ETOs, MLPs and GLPs is the self-frictional quantum forces which are analog of radiation damping or self-frictional forces introduced by Lorentz in classical electrodynamics. The relations for the quantum self-frictional potentials in terms of ETOs, MLPs and GLPs, respectively, are established. We note that, in the case of disappearing frictional forces, the ETOs are reduces to the oringers wave functions for the hydrogen-like atoms in standard convention and, therefore, become the noncomplete.