A redefinition of quantum-mechanical exchange and Coulomb integrals by a reinterpretation of atomic and molecular orbitals as Taylor expansions of a potential and a similar treatment of the electromagnetic field.

Abstract

In previous papers a deterministic account of the dynamics underlying i) the Schrodinger equation, ii) the commutation relations of quantum theory and Planck's constant and iii) theS-matrix and the Klauder phenomenon, was presented. In the present paper, that topological analysis is extended to a deterministic interpretation of atomic orbitals, valence bonds, molecular orbitals and the electromagnetic field. It is demonstrated that atomic orbitals may be considered ask-jets, or the polynomial consisting of all terms of order less than or equal tok in the Taylor expansion of a potential function. The electromagnetic field is described in terms of a mapping of two sets of four Clebsch potentials defined on a four-dimensional Riemannian space-time manifold, onto a three-dimensional Euclidean space (Rund). The Clebsch potentials are related to the four parameters used in the quantum-mechanical orbital description.