Schrödinger Theory from the Perspective of ‘Classical’ Fields Derived from Quantal Sources

Abstract

In order to understand quantal density functional theory (Q-DFT), it is necessary to first understand Schrödinger theory [1] from the perspective of ‘classical’ fields and their quantal sources [2]. The terminology ‘classical’ is employed in the original sense of fields as pervading all space, and not necessarily as solutions of Maxwell’s equations. The description of a quantum system, and of its energy and energy components in terms of fields, provides a new perspective on Schrödinger theory, one that is physically tangible. This different perspective, however, still lies within the rubric of the theory’s probabilistic description of a quantum system in that the sources of the fields are quantum mechanical expectations of Hermitian operators taken with respect to the system wavefunction. Thus, these fields may be thought of as being inherent to the quantal system, (just as the solution to Maxwell’s equations are inherent to an electromagnetic system), with each field, or sum of fields, contributing to a specific energy component. This chapter is a description of Schrödinger theory from this perspective of fields and quantal sources. The equivalence of Schrödinger theory as described by its field perspective to the corresponding Euler equation of Quantum Fluid Dynamics is also derived.