Shift operators and recurrence relations for Legendre polynomials with noninteger associativity and definite parity

Eugenio Ley-Koo () and Salvador A. Cruz ()
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Eugenio Ley-Koo: Universidad Nacional Autnoma de México, Instituto de Física
Salvador A. Cruz: Universidad Autnoma Metropolitana-Iztapalapa, Departamento de Física

A chapter in Physical and Mathematical Aspects of Symmetries, 2017, pp 233-238 from Springer

Abstract: Abstract This is the written version of new results reported at Gr31 in our contribution “O(2) Symmetry Breaking in Dihedrally Confined Atoms and Consequent Modifications of the Periodic Table”. It is focused on identifying new shift operators and recurrence relations for Legendre polynomials with noninteger asociativities and definite parities, due to the dihedral confinement and its O(2) symmetry breaking. Recurrence relations play a key role in evaluating the two-electron matrix elements of their Coulomb repulsion multipole components in the Hartree-Fock calculations for the confined atoms.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-69164-0_35

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DOI: 10.1007/978-3-319-69164-0_35

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