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American Journal of Physics

Allowed values of J in j j coupling of equivalent electrons

E. R. Tuttle

Published Jul 1, 1980• 4 citations
Publisher

Abstract

A simple method is given for finding the values of the total angular momentum J for configurations of equivalent electrons in jj coupling. It is also shown how a knowledge of both the LS and jj terms can contribute to the student’s understanding of the role of different representations in elementary quantum mechanics. Because the principles and the computations required are elementary, this material is particularly suitable for presentation to undergraduates and to graduate students taking a first course in quantum mechanics.

DOI
10.1119/1.12057

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A simple method is given for finding the values of the total angular momentum J for configurations of equivalent electrons in jj coupling. It is also shown how a knowledge of both the LS and jj terms can contribute to the student’s understanding of the role of different representations in elementary quantum mechanics. Because the principles and the computations required are elementary, this material is particularly suitable for presentation to undergraduates and to graduate students taking a first course in quantum mechanics.
A simple method is given for finding the terms obtained from a configuration containing a number of equivalent electrons. This method is based entirely upon two facts: (1) the Pauli principle prevents any two electrons from having the same quantum numbers; and, (2) one and only one completely antisymmetric wavefunction can be constructed from any given set of allowed quantum numbers. Because of its simplicity, both in concept and in application, this system is well suited to presentation to undergraduate students of modern physics.
Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB approximations and Bohr-Sommerfeld quantization. Important modern topics and examples are also described, including Berry phase, quantum information, complexity and chaos, decoherence and thermalization, nonstandard statistics, as well as more advanced material such as path integrals, scattering theory, multiparticles and Fock space. Readers will gain a broad overview of Quantum Mechanics, as solid preparation for further study or research.
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Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB approximations and Bohr-Sommerfeld quantization. Important modern topics and examples are also described, including Berry phase, quantum information, complexity and chaos, decoherence and thermalization, nonstandard statistics, as well as more advanced material such as path integrals, scattering theory, multiparticles and Fock space. Readers will gain a broad overview of Quantum Mechanics, as solid preparation for further study or research.
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