Schrödinger Theory from a “Newtonian” Perspective

Abstract

Time-independent quantal density functional theory (Q-DFT) [1] is a description of the mapping from a system of electrons in an external field in their ground or excited state as described by Schrodinger theory, to a model system of noninteracting fermions – the S system – whereby the equivalent density ρ(r), the energy E, and the ionization potential I are obtained. The reason for the mapping to the model S system is that for a system of N electrons, it is easier to solve the corresponding N model-fermion single-particle differential equations than it is to solve the single N-electron Schrodinger equation. The model system is described by Q-DFT via a “Newtonian” perspective. This perspective is in terms of fields that are “classical” in nature and which pervade all space, but whose sources are quantal in that they are quantum-mechanical expectations of Hermitian operators or of the complex sum of Hermitian operators. As the model system is in effect a representation of the interacting system, it is best to first describe Schrodinger theory [2] from the same “Newtonian” perspective of “classical” fields and quantal sources [3, 4]. This perspective of Schrodinger theory is new. To quote from Einstein and Infeld [5]: “A new concept appeared in physics, the most important invention since Newton’s time: the field. It needed great scientific imagination to realize that it is not the charges nor the particles but the field in the space between the charges and particles that is essential for the description of the physical phenomenon.” These remarks were made with reference to the classical physics of Faraday and Maxwell. Einstein and Infeld may not have imagined then that nonrelativistic QuantumMechanics/Schrodinger theory too could be similarly described in terms of fields that are “classical” in nature but which arise from sources that are quantal.