Schrödinger-Pauli Theory of Electrons: New Perspectives

The Schrödinger-Pauli (SP) equation corresponds to a system of
N electrons in an electrostatic E (r) = - ▽ v (r) and a magnetostatic field
B (r) = ▽ x A (r) in which the interaction of the latter with both the orbital
and spin angular momentum is incorporated. The `Quantal Newtonian' first
law for the SP equation is derived: the sum of the external F^ext (r) and
internal F^int (r) fields acting on each electron vanishes. The external field
is the sum of the electrostatic and Lorentz fields. The internal field is a sum
of fields representative of the Pauli exclusion principle and Coulomb repulsion,
kinetic effects, the density, and the magnetic field. From the law, it is shown
that the SP equation is intrinsically self-consistent. A Quantal Density
Functional Theory of the mapping from the interacting system to one of
noninteracting fermions possessing the same density and physical current
density is developed.