Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries
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 ne...
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| Format: | Article |
| Language: | English |
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MDPI AG
2012-11-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/4/4/667 |
| _version_ | 1811304253264756736 |
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| author | Renato Lemus |
| author_facet | Renato Lemus |
| author_sort | Renato Lemus |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T08:02:45Z |
| format | Article |
| id | doaj.art-c3675a529329435dba8cdd241e74c999 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T08:02:45Z |
| publishDate | 2012-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c3675a529329435dba8cdd241e74c9992022-12-22T02:55:14ZengMDPI AGSymmetry2073-89942012-11-014466768510.3390/sym4040667Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete SymmetriesRenato LemusThe 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.http://www.mdpi.com/2073-8994/4/4/667quantum numbersdiscrete systemssymmetry projectioneigenfunction methodH+3CH4 |
| spellingShingle | Renato Lemus Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries Symmetry quantum numbers discrete systems symmetry projection eigenfunction method H+3 CH4 |
| title | Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries |
| title_full | Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries |
| title_fullStr | Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries |
| title_full_unstemmed | Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries |
| title_short | Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries |
| title_sort | quantum numbers and the eigenfunction approach to obtain symmetry adapted functions for discrete symmetries |
| topic | quantum numbers discrete systems symmetry projection eigenfunction method H+3 CH4 |
| url | http://www.mdpi.com/2073-8994/4/4/667 |
| work_keys_str_mv | AT renatolemus quantumnumbersandtheeigenfunctionapproachtoobtainsymmetryadaptedfunctionsfordiscretesymmetries |