Schrodinger theory from the perspective of classical fields derived from quantal sources

In this paper we describe Schrodinger theory from the perspective of classi cal fields whose sources are quantal expectations of Hermitian operators. A s such these fields may be considered as being intrinsic to and thereby des criptive of the quantum system. The perspective is valid for both ground an d bound excited-states. The fields, whose existence is inferred via the dif ferential virial theorem, are as follows: (i) an electron-interaction field E-ee(r,t) derived via Coulomb's law from the pair-correlation density; (ii ) a kinetic-field L(r,t) derived as the derivative of the kinetic-energy-de nsity tensor obtained from the spinless single-particle density matrix; (ii i) a differential density field D(r,t) which is the gradient of the Laplaci an of the electron density; and (iv) a current-density field J(r,t) derived as the time derivative of the current density whose source too is the spin less single-particle density matrix. The total energy and its components ma y be expressed in terms of these fields: the electron-interaction potential and kinetic energies via the fields E-ee(r,t) and L(r,t), respectively, an d the external potential energy via a conservative field which is the sum o f all the fields present. The field perspective is illustrated by applicati on to the exactly solvable stationary ground-state of the Hooke's atom, its extension to the time-dependent case being surmised via the Harmonic Poten tial theorem. Finally, we note that both Schrodinger and Kohn-Sham density- functional theory are now describable in terms of classical fields derived from quantal sources. (C) 2000 Elsevier Science B.V. All rights reserved.