Schrödinger-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 the new perspective of the individual electron via its equation of motion or ‘Quantal Newtonian’ first law. 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 electron correlations due to the Pauli principle and Coulomb repulsion, the electron density, kinetic effects, and the physical current density. The energy can be expressed in integral virial form in terms of these fields. The law leads to the understanding that the Hamiltonian is an exactly known and universal functional of the wave function. This generalizes the SP equation, and 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.
Sahni, Viraht, "New Perspectives on the Schrödinger-Pauli Theory of Electrons: Part I" (2019). CUNY Academic Works.