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Journal of Changsha University

Octonion Quantum Mechanics and the Exclusion Principle

Wang Hongji

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

In this paper firstly the octonion quantum mechanics theory was introduced ,then by using the octonion quantum mechanics theory the Zeeman effect was researched and finally the Pauling exclusion principle was deduced.

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Cambridge University Press eBooks•Aug 4, 2005•0 citations
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.
Abstract The exclusion principle is one of the most far-reaching theorems in physics. In a telegram to the Nobel committee, quoted in [1], Einstein wrote: ‘Nominate Wolfgang Pauli for physics prize stop his contributions to modern quantum theory consisting of so-called Pauli or exclusion principle became fundamental part of modern physics being independent from other basic axioms of that theory stop Albert Einstein.’ It is interesting to note that quantum mechanics, the theory Einstein alluded to, was formulated a little after the Pauli principle.
The modern state of the Pauli exclusion principle is shortly discussed. We describe the discovery by Pauli, his principle for electrons, and how it was generalized for all elementary particles in the framework of quantum mechanics. The motivations and theoretical conceptions that induced the experiments for verification of the Pauli exclusion principle are analyzed. The results and methodology of two different types of experiments are discussed: (1) the search of unusual atoms and nuclei in the stable non-Pauli states, and (2) the experiments in which the emitted radiation of non-Pauli transitions is measured. In conclusion, the comments on the discussed experiments that follow from the general quantum mechanical conceptions and group theory are formulated.
The exclusion principle was the final outcome of Pauli's struggle to understand some spectroscopic anomalies in the early 1920s: doublets were observed in the spectra of alkali metals, singlets and triplets in the spectra of the alkaline earths, and even more anomalous patterns were observed when chemical elements were placed in an external magnetic field (anomalous Zeeman effect and Paschen–Back effect). These anomalous spectra challenged the old quantum theory, and prompted a radical theoretical change (Section 2.1). From 1920 to 1924 Alfred Landé, Werner Heisenberg, and Niels Bohr were all engaged in trying to save the traditional spectroscopic model (the so-called atomic core model) and to reconcile it with the observed anomalies. The impasse was solved only with Pauli's introduction of a fourth degree of freedom for the electron, and the consequent demise of the atomic core model (Section 2.2). What Pauli called the ‘twofoldness’ [ Zweideutigkeit ] of the electron's angular momentum was soon reinterpreted as the electron's spin (Section 2.3). Pauli's exclusion rule was announced in this semi-classical spectroscopic context that characterized the revolutionary transition from the old quantum theory to the new quantum theory around 1925. The prehistory of Pauli's exclusion principle Atomic spectra and the Bohr–Sommerfeld theory of atomic structure The existence of spectral lines had been known to scientists since the beginning of the nineteenth century when Wollaston and Fraunhofer first observed the dark absorption lines in the spectrum of the Sun.
Shortly after their introduction, the electron's Zweideutigkeit and Pauli's Ausschliessungsregel were embedded into a growing theoretical framework: from Fermi–Dirac statistics in 1926 (Section 4.2), to the non-relativistic quantum mechanics of the magnetic electron with Pauli's spin matrices in 1927 (Section 4.3); from Wigner and von Neumann's group theoretical derivation of the spin matrices in 1927 (Section 4.4), to Jordan's reinterpretation of Pauli's exclusion principle in terms of anticommutation relations for particle creation and annihilation operators in 1928 (Section 4.5), which paved the way for quantum field theory. The most important step in building up this theoretical framework was the transition from non-relativistic to relativistic quantum mechanics, with Dirac's equation for the electron in 1928 (Section 4.6), which finally allowed the derivation of the electron's spin with its anomalous magnetic moment and hence clarified in a conclusive way the origin of spectroscopic anomalies. The negative energy solutions of the Dirac equation, and Dirac's attempt to accommodate them via the hole theory in 1930, anticipated the experimental discovery of the antiparticle of the electron, the positron. Sections 4.7-4.9 reconstruct Pauli's sustained criticism of Dirac's hole theory. The history of this debate is intertwined with Pauli's search for a spin–statistics connection, which finally culminated in the spin–statistics theorem in 1940. With this theorem, the nomological shift from the status of a phenomenological rule to that of a fundamental scientific principle is finally completed. Introduction The year 1925 was the annus mirabilis for quantum mechanics.