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International Journal of Quantum Chemistry

Information theory interpretation of the Pauli principle and Hund rule

Danail Bonchev

Published Apr 1, 1981• 14 citations
Publisher

Abstract

Abstract Making use of different information measures, the Pauli exclusion principle and the first Hund rule were found to be related to a trend toward acquiring a maximum information content of the atoms and molecules, and more generally, for any fermion system. The bosons conversely always have a minimum (zero) information content with respect to the permutation symmetry of their wave functions. Some new interpretations of the Pauli principle are presented.

DOI
10.1002/qua.560190418

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Abstract Making use of different information measures, the Pauli exclusion principle and the first Hund rule were found to be related to a trend toward acquiring a maximum information content of the atoms and molecules, and more generally, for any fermion system. The bosons conversely always have a minimum (zero) information content with respect to the permutation symmetry of their wave functions. Some new interpretations of the Pauli principle are presented.
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This is the first scientific book devoted to the Pauli Exclusion Principle, which is a fundamental principle of quantum mechanics and is permanently applied in chemistry, physics, molecular biology and in physical astronomy. However, while the principle has been studied for more than 90 years, rigorous theoretical foundations still have not been established and many unsolved problems remain. Following an introduction and historical survey, this book discusses the still unresolved questions around this fundamental principle. For instance, why, according to the Pauli Exclusion Principle, are only symmetric and antisymmetric permutation symmetries for identical particles realized, while the Schrödinger equation is satisfied by functions with any permutation symmetry? Chapter 3 covers possible answers to this, while chapter 4 presents effective and elegant methods for finding the Pauli-allowed states in atomic, molecular and nuclear spectroscopy. Chapter 5 discusses parastatistics and fractional statistics, demonstrating that the quasiparticles in a periodical lattice, including excitons and magnons, are obeying modified parafermi statistics. With detailed appendices, The Pauli Exclusion Principle: Origin, Verifications and Applications is intended as a self-sufficient guide for graduate students and academic researchers in the fields of quantum mechanics, theoretical chemistry, physics, and applied mathematics. It will be a valuable resource for any reader interested in the foundations of quantum mechanics and its applications in areas such as atomic and molecular spectroscopy, spintronics, molecular biology, and applied fields of quantum information.
The Pauli exclusion principle is one of the fundamental laws of modern physics. It determines the structure of atoms, the stability of matter, the properties of fermionic systems, and macroscopic phenomena ranging from chemistry to astrophysics. In standard quantum mechanics (QM), this principle is formulated as an axiom of antisymmetry: the wave function of two fermions must change sign under the exchange of coordinates. However, the origin of this antisymmetry remains unexplained within QM itself. Within ZEBTS — the Law of Unity of Being of the Triune Substance — the Pauli principle acquires a geometric and topological foundation. In this ontology, fermions are not treated as elementary particles but as topological modes of the operator metric, arising from the spectral structure of quantum geometry. Antisymmetry and the prohibition of identical states emerge as consequences of: the non‑commutativity of the operator metric, the topological charge λ, the spectral non‑intersection of eigenvalues, holographic constraints on information density. Thus, ZEBTS derives the Pauli principle as a topological law of quantum geometry, rather than a postulate.
Both bosons and fermions satisfy a strong version of Leibniz’s Principle of the Identity of Indiscernibles (PII), and so are ontologically on a par with respect to the PII. This holds for non-entangled, non-product states and for physically entangled states—as it has been established in previous work. In this paper, the Leibniz strategy is completed by including the (bosonic) symmetric product states. A new understanding of Pauli’s Exclusion Principle is provided, which distinguishes bosons from fermions in a peculiar ontological way. Finally, the program as a whole is defended against substantial objections.