An outline is given of current advances on some basic ingredients of applied quantum mechanics, that were previously developed along different lines and are now being compacted within a unifying framework. Specifically, (i) complete orthogonal expansion basis sets for the atomic and molecular orbitals of quantum chemistry are classified within angular momentum theory, presently incorporated in and generalized as spin network theory; (ii) spin-networks and the underlying theory of hypergeometrical polynomials are presented within a graphical approach; (iii) the combinatorial significance of the graphical approach is given a projective geometry foundation; (iv) emergence and role of hidden (Regge's) symmetries are revealed and discussed in a variety of contexts.

Spin networks and sturmian orbitals: Orthogonal complete polynomial sets in molecular quantum mechanics

Coletti, Cecilia;
2017-01-01

Abstract

An outline is given of current advances on some basic ingredients of applied quantum mechanics, that were previously developed along different lines and are now being compacted within a unifying framework. Specifically, (i) complete orthogonal expansion basis sets for the atomic and molecular orbitals of quantum chemistry are classified within angular momentum theory, presently incorporated in and generalized as spin network theory; (ii) spin-networks and the underlying theory of hypergeometrical polynomials are presented within a graphical approach; (iii) the combinatorial significance of the graphical approach is given a projective geometry foundation; (iv) emergence and role of hidden (Regge's) symmetries are revealed and discussed in a variety of contexts.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11564/685490
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