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

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

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Received: 1 August 2012; in revised form: 23 November 2012 / Accepted: 26 November 2012 / Published: 30 November 2012
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Keywords: quantum numbers; discrete systems; symmetry projection; eigenfunction method; H+3 ; CH4
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MDPI and ACS Style

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

AMA Style

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

Chicago/Turabian Style

Lemus, Renato. 2012. "Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries." Symmetry 4, no. 4: 667-685.

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