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

In previous papers a deterministic account of the dynamics underlying i) the Schrödinger equation, ii) the commutation relations of quantum theory and Planck's constant and iii) the S-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 as k-jets, or the polynomial consisting of all terms of order less than or equal to k 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. © 1979 Società Italiana di Fisica.