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The self-frictional field of electrons remains one of the most important problems of the classical and quantum physics to date, therefore, it is to be examined theoretically and experimentally by scientists as an actual problem. This study aims to the recent important developments in the examination of the quantum self-frictional field, which is one of the most important old problems of physics, and the research direction that needs to be examined in the future is included. In this study, we have presented a detailed explanation of the physical nature of quantum self-frictional atomic field potentials, including enhancements and developments on the significant subject. A complete understanding of classical and quantum self-frictional field potential and force, have been carefully examined., Comment: 8 pages

An efficient calculation method is proposed for the face centered cubic (FCC) lattice Green function. The method is based on binomial expansion theorems, which is provide us establish analytical formulae through simple basic integrals. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the lattice Green function are in good agreement with the known numerical calculation results., Comment: 4 pages

In this study, using the analytical and recurrence relations suggested by the authors in previous works, the new efficient and reliable program procedure for the overlap integrals over Slater type orbitals (STOs) is presented. The proposed procedure guarantees a highly accurate evaluation of the overlap integrals with arbitrary values of quantum numbers, screening constants and internuclear distances. It is demonstrated that the computational accuracy of the proposed procedure is not only dependent on the efficiency of formulas, as has been discussed previously, but also on a number of other factors including the used program language package and solvent properties. The numerical results obtained using the algorithm described in the present work are in a complete agreement with those obtained using the alternative evaluation procedure. We notice that the program works without any restrictions and in all range of integral parameters., Comment: 6 pages, 2 tables