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Symmetry 2012, 4(4), 667-685; doi:10.3390/sym4040667

Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries

Institute of Nuclear Physics, Autonomous National University of Mexico, A.P. 70-543, Circuito Exterior, C.U., México, D.F. 04510, Mexico
Received: 1 August 2012 / Revised: 23 November 2012 / Accepted: 26 November 2012 / Published: 30 November 2012
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Abstract

The eigenfunction approach used for discrete symmetries is deduced from the concept of quantum numbers. We show that the irreducible representations (irreps) associated with the eigenfunctions are indeed a shorthand notation for the set of eigenvalues of the class operators (character table). The need of a canonical chain of groups to establish a complete set of commuting operators is emphasized. This analysis allows us to establish in natural form the connection between the quantum numbers and the eigenfunction method proposed by J.Q. Chen to obtain symmetry adapted functions. We then proceed to present a friendly version of the eigenfunction method to project functions. View Full-Text
Keywords: quantum numbers; discrete systems; symmetry projection; eigenfunction method; H+3 ; CH4 quantum numbers; discrete systems; symmetry projection; eigenfunction method; H+3 ; CH4
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Lemus, R. Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries. Symmetry 2012, 4, 667-685.

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