Quantum‐Mechanical Definition of the Classical Scalar Potential in Schrödinger‐Pauli and Schrödinger Theory

According to the Bohr correspondence principle, the external temporal scalar potential in the classical equation of motion is replicated in quantum theory as a multiplicative operator. An equivalent quantum‐mechanical definition of the scalar potential in Schrödinger‐Pauli/Schrödinger theory is provided. The potential is a known universal functional of the wave function. At each instant of time, it is the work done in a conservative “classical” field representative of internal properties of the system: Pauli and Coulomb correlations, kinetic effects, the density, the Lorentz force, an internal magnetic component, and the current density response. The Hamiltonians are thus rewritten in a new physical manner indicative of these properties. An application to the triplet state of a 2‐electron semiconductor quantum dot in a magnetic field is provided. The significance of the definition to the Hohenberg‐Kohn theorem, and its relationship to Quantum and Kohn‐Sham density functional theory, is discussed.