@article{SIGMA_2017_13_a37,
author = {Eugene D. Belokolos},
title = {Mendeleev {Table:} a {Proof} of {Madelung} {Rule} and {Atomic} {Tietz} {Potential}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2017},
volume = {13},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a37/}
}
Eugene D. Belokolos. Mendeleev Table: a Proof of Madelung Rule and Atomic Tietz Potential. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a37/
[1] Abel N. H., “Solution de quelques problémes à l'aide d'intégrales définies”, {ØE}uvres completes de Niels Henrik Abel (Christiania, Norway, 1881), eds. L. Sylow, S. Lie, 11–27 | MR
[2] Allen L. C., Knight E. T., “The Löwdin challenge: origin of the $n+l,n$ (Madelung) rule for filling the orbital configurations of the periodic table”, Int. J. Quantum Chem., 90 (2002), 80–88 | DOI
[3] Arnol'd V.I., Mathematical methods of classical mechanics, 3rd ed., Nauka, M., 1989 | MR | Zbl
[4] Bacry H., Ruegg H., Souriau J. M., “Dynamical groups and spherical potentials in classical mechanics”, Comm. Math. Phys., 3 (1966), 323–333 | DOI | MR | Zbl
[5] Bargmann V., “Zur Theorie des Wasserstoffatoms”, Bemerkungen zur gleichnamigen Arbeit von V. Fock, 99 (1936), 576–582 | DOI
[6] Belokolos E. D., “The integrability and the structure of atom”, J. Math. Phys. Anal. Geometry, 9 (2002), 339–351 | MR | Zbl
[7] Demkov Y. N., Ostrovskii V. N., “Internal symmetry of the Maxwell “fish eye” problem and the Fock group for the hydrogen atom”, Sov. Phys. JETP, 33 (1971), 1083–1087
[8] Fermi E., “Über die Anwendung der statistischen Methode auf die Probleme des Atombaues”, Quantentheorie und Chemie, ed. H. Falkenhagen, Leipziger Vorträge, S. Hirzel-Verlag, Leipzig, 1928, 95–111 | Zbl
[9] Fock V., “Zur Theorie des Wasserstoffatoms”, Z. Phys., 98 (1935), 145–154 | DOI
[10] Fradkin D. M., “Existence of the dynamic symmeries ${\rm O}(4)$ and ${\rm SU}_{3}$ for all classical central potential problems”, Progr. Theoret. Phys., 37 (1967), 798–812 | DOI | Zbl
[11] Hakala R., “The periodic law in mathematical form”, J. Phys. Chem., 56 (1952), 178–181 | DOI
[12] Ivanenko D., Larin S., “Theory of periodic system of elements”, Dokl. Akad. Nauk USSR, 88 (1953), 45–48
[13] Kibler M. R., On a group-theoretical approach to the periodic table of chemical elements, arXiv: quant-ph/0408104
[14] Kibler M. R., From the Mendeleev periodic table to particle physics and back to the periodic table, arXiv: quant-ph/0611287
[15] Klechkovski V. M., The distribution of atomic electrons and the filling rule for $(n + l)$-groups, Atomizdat, M., 1968
[16] Landau L. D., Lifshits E. M., Theoretical physics, v. 1, Mechanics, Nauka, M., 1973 | MR
[17] Landau L. D., Lifshits E. M., Theoretical physics, v. 3, Quantum mechanics: nonrelativistic theory, Nauka, M., 1974 | MR
[18] Latter R., “Atomic energy levels for the Thomas–Fermi and Thomas–Fermi–Dirac potentials”, Phys. Rev., 99 (1955), 510–519 | DOI
[19] Lenz W., “Zur Theorie der optischen Abbildung”, Probleme der mathematischen Physik, Leipzig, 1928, 198–207 | Zbl
[20] Lieb E. H., “Thomas–Fermi and related theories of atoms and molecules”, Rev. Modern Phys., 53 (1981), 603–641 | DOI | MR
[21] Lieb E. H., Simon B., “The Thomas–Fermi theory of atoms, molecules and solids”, Adv. Math., 23 (1977), 22–116 | DOI | MR | Zbl
[22] Madelung E., Die mathematischen Hilfsmittel des Physikers, Die Grundlehren der Mathematischen Wissenschaften, 4, Springer-Verlag, Berlin, 1936 | DOI | MR
[23] Maxwell J. C., “Solutions of problems”, The Scientific Papers of James Clerk Maxwell, ed. W. D. Niven, Dover Publications, New York, 1952, 76–79 | MR
[24] Meek T. I., Allen L. C., “Configuration irregularities: deviations from the Madelung rule and inversion of orbital energy levels”, Chem. Phys. Lett., 362 (2002), 362–364 | DOI
[25] Mukunda N., “Dynamical symmeries and classical mechanics”, Phys. Rev., 155 (1967), 1383–1386 | DOI
[26] Ostrovsky V. N., “Dynamic symmetry of atomic potential”, J. Phys. B: At. Mol. Phys., 14 (1981), 4425–4439 | DOI
[27] Ostrovsky V. N., What and how physics contributes to understanding the periodic law?, Found. Chem., 3 (2001), 145–182 | DOI
[28] Pauli W., “Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik”, Z. Phys., 36 (1926), 336–363 | DOI | Zbl
[29] Reed M., Simon B., Methods of modern mathematical physics, v. IV, Analysis of operators, Academic Press, New York–London, 1978 | MR | Zbl
[30] Tietz T., “Über eine Approximation der Fermischen Verteilungsfunktion”, Ann. Physik, 450 (1955), 186–188 | DOI | MR
[31] Tietz T., “Elektronengruppen im periodischen System der Elemente in der statistischen Theorie des Atoms”, Ann. Physik, 460 (1960), 237–240 | DOI | MR
[32] Tietz T., “Über Eigenwerte und Eigenfunktionen der Schrödinger-Gleichung für das Thomas–Fermische Potential”, Acta Phys. Acad. Sci. Hungar., 11 (1960), 391–400 | DOI | MR
[33] Torrielli A., “Classical integrability”, J. Phys. A: Math. Theor., 49 (2016), 323001, 31 pp., arXiv: 1606.02946 | DOI | MR | Zbl
[34] Wong D. P., “Theoretical justification of Madelung's rule”, J. Chem. Educ., 56 (1979), 714–717 | DOI