Representation theory of finite abelian groups applied to a linear diatomic crystal
After a brief review of matrix representations of finite abelian groups, projection operators are defined and used to compute symmetry coordinates for systems of coupled harmonic oscillators. The Lagrangian for such systems is discussed in the event that the displacements along the symmetry coordina...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1980-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171280000427 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548676385374208 |
|---|---|
| author | J. N. Boyd P. N. Raychowdhury |
| author_facet | J. N. Boyd P. N. Raychowdhury |
| author_sort | J. N. Boyd |
| collection | DOAJ |
| description | After a brief review of matrix representations of finite abelian groups, projection operators are defined and used to compute symmetry coordinates for systems of coupled harmonic oscillators. The Lagrangian for such systems is discussed in the event that the displacements along the symmetry coordinates are complex. Lastly, the natural frequencies of a linear, diatomic crystal are determined through application of the Born cyclic condition and the determination of the symmetry coordinates. |
| format | Article |
| id | doaj-art-6acd7b6849bd4be6bc27eec85e917a85 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6acd7b6849bd4be6bc27eec85e917a852025-02-03T06:13:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013355957410.1155/S0161171280000427Representation theory of finite abelian groups applied to a linear diatomic crystalJ. N. Boyd0P. N. Raychowdhury1Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284, Virginia, USADepartment of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284, Virginia, USAAfter a brief review of matrix representations of finite abelian groups, projection operators are defined and used to compute symmetry coordinates for systems of coupled harmonic oscillators. The Lagrangian for such systems is discussed in the event that the displacements along the symmetry coordinates are complex. Lastly, the natural frequencies of a linear, diatomic crystal are determined through application of the Born cyclic condition and the determination of the symmetry coordinates.http://dx.doi.org/10.1155/S0161171280000427abelian groupsBorn cyclic conditiongroup representationsharmonic oscillatorsLagrangian mechanicsnatural frequenciesprojection operators. |
| spellingShingle | J. N. Boyd P. N. Raychowdhury Representation theory of finite abelian groups applied to a linear diatomic crystal International Journal of Mathematics and Mathematical Sciences abelian groups Born cyclic condition group representations harmonic oscillators Lagrangian mechanics natural frequencies projection operators. |
| title | Representation theory of finite abelian groups applied to a linear diatomic crystal |
| title_full | Representation theory of finite abelian groups applied to a linear diatomic crystal |
| title_fullStr | Representation theory of finite abelian groups applied to a linear diatomic crystal |
| title_full_unstemmed | Representation theory of finite abelian groups applied to a linear diatomic crystal |
| title_short | Representation theory of finite abelian groups applied to a linear diatomic crystal |
| title_sort | representation theory of finite abelian groups applied to a linear diatomic crystal |
| topic | abelian groups Born cyclic condition group representations harmonic oscillators Lagrangian mechanics natural frequencies projection operators. |
| url | http://dx.doi.org/10.1155/S0161171280000427 |
| work_keys_str_mv | AT jnboyd representationtheoryoffiniteabeliangroupsappliedtoalineardiatomiccrystal AT pnraychowdhury representationtheoryoffiniteabeliangroupsappliedtoalineardiatomiccrystal |