Quantum-Dynamical Theory of Electron Exchange Correlation

Abstract

The relationship between the spin of an individual electron and Fermi-Dirac statistics (FDS), which is obeyed by electrons in the aggregate, is elucidated. The relationship depends on the use of spin-dependent quantum trajectories (SDQT) to evaluate Coulomb's law between any two electrons as an instantaneous interaction in space and time rather than as a quantum-mean interaction in the form of screening and exchange potentials. Hence FDS depends in an ab initio sense on the inference of SDQT from Dirac's equation, which provides for relativistic Lorentz invariance and a permanent magnetic moment (or spin) in the electron's equation of motion. Schroedinger's time-dependent equation can be used to evaluate the SDQT in the nonrelativistic regime of electron velocity. Remarkably FDS is a relativistic property of an ensemble of electron, even though it is of order 0 in the nonrelativistic limit, in agreement with experimental observation. Finally it is shown that covalent versus separated-atoms limits can be characterized by the SDQT. As an example of the use of SDQT in a canonical structure problem, the energies of the 1 Σ and 3 Σ states of H 2 are calculated and compared with the accurate variational energies of Kolos and Wolniewitz.

Compatibility of Quantum Entanglement with the Special Theory of Relativity

“…It is well known that a physically correct many-electron wave function in orbital and spin space must be antisymmetric with respect to electron exchange, which is a mathematical recipe to guarantee the Pauli Exclusion Principle and to reconstruct the dynamical information which is otherwise lost in stationary-state theory. The Pauli Exclusion Principle and Fermi-Dirac statistics have only recently been demonstrated on an ab initio basis using a dynamical quantum theory of electron exchange-correlation in space and time [5] [6]. In this paper, I show that the previous work [5] [6] also provides an understanding in a dynamical sense of quantum entanglement and disentanglement.…”

Use of Quantum Trajectories in Computational Molecular Bioscience

“…Should computational resources continue to be devoted to the further implementation of approximate methods of molecular electronic structure? In this brief report, I point out that a first-principles theory for electron exchange-correlation based on a quantum trajectory methodology has been available in principle since Dirac's 1928 paper for a relativistic electron but has not been implemented until recently [1] [2] owing to the ascendancy of Schroedinger theory in the intervening years. This neglect appears to originate with the canard that Schroedinger theory is valid except in the regime of high electron velocity in a high-Z regime of atomic structure.…”