New Complete Orthonormal Sets of Exponential-Type Orbitals in Standard Convention and Their Origin

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.