New Perspectives on the Schr{\"o}dinger-Pauli Theory of Electrons: Part I

TL;DR

This paper introduces a new perspective on Schr{"o}dinger-Pauli theory by analyzing individual electrons through their equations of motion, leading to novel insights and a functional approach to the system's energy components.

Contribution

It presents a new physical and mathematical framework for Schr{"o}dinger-Pauli theory based on the electron's equation of motion and develops a quantal density functional theory for the system.

Findings

The law describes the electron's experience of external and internal fields.

The energy components are expressed in integral virial form.

The Hamiltonian is a known functional of the wave function.

Abstract

Schr{\"o}dinger-Pauli (SP) theory is a description of electrons in the presence of a static electromagnetic field in which the interaction of the magnetic field with both the orbital and spin moments is explicitly considered. The theory is described from a new perspective, viz. that of the individual electron via its equation of motion or `Quantal Newtonian' first law. The law leads to new physical and mathematical insights into the theory. The law is in terms of `classical' fields whose sources are quantum mechanical expectation values of Hermitian operators taken with respect to the system wave function. The law states that each electron experiences an external and an internal field, the sum of which vanish. The external field is the sum of the electrostatic and a Lorentz field. The internal field is a sum of fields: the electron-interaction, differential density, kinetic, and internal magnetic fields. These fields are respectively representative of a property of the system: electron correlations due to the Pauli exclusion principle and Coulomb repulsion, the electron density, kinetic effects, and the physical current density. The energy components can be expressed in integral virial form in terms of these fields. The law leads to the further understanding that the Hamiltonian is an exactly known and universal functional of the wave function. This allows for the generalization of the SP equation, which then proves it to be intrinsically self-consistent. A Quantal density functional (local effective potential) theory of the SP system is developed. Further generalizations of the present work to the temporal case, and relativistic Dirac theory are proposed.