DOI: 10.1098/rsta.1963.0002. On the symmetries of spherical harmonics

On the symmetries of spherical harmonics

10.1098/rsta.1963.0002

Crossref journal-article

The Royal Society

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences (175)

Abstract

This paper extends the work described in a previous paper by one of the authors (Altmann 1957). The spherical harmonics that belong to the irreducible representations of the cubic groups are now given up to and including l = 12. Also, for all point groups the expansions in spherical harmonics that are given belong to the separate columns of the irreducible representations (whereas before they were linear combinations of such functions). Accordingly, full tables for the irreducible representations for all crystallographic point groups are required and are given in the paper. Finally, a technique is described, and used throughout in the tables, to orthogonalize several expansions that belong to the same column of the same irreducible representation. Therefore, the different expansions listed in the tables are always fully orthogonal.

Bibliography

On the symmetries of spherical harmonics. (1963). Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 255(1054), 199â215.

Authors 0

None

References 4 Referenced 54

{'key': 'p_1', 'first-page': '343', 'article-title': 'Proc. Camb. P h i l', 'volume': '53', 'author': 'Itm', 'year': '1957', 'journal-title': 'Soc.'} / Soc. / Proc. Camb. P h i l by Itm (1957)
A Itm ann 8. L. 1962a G roup theory in Quantum theory (ed. D. R . Bates) vol. 2 p. 87. New York: A cadem ic Press.
A Itm ann 8. L. 19626
{'key': 'p_4', 'first-page': '216', 'volume': '255', 'author': 'Itm', 'year': '1962', 'journal-title': 'Phil. Trans. A'} / Phil. Trans. A by Itm (1962)

Dates

Type	When
Created	18 years, 8 months ago (Dec. 15, 2006, 5:43 p.m.)
Deposited	4 years, 6 months ago (Feb. 18, 2021, 5:56 p.m.)
Indexed	1 year, 2 months ago (June 7, 2024, 10:43 a.m.)
Issued	62 years, 7 months ago (Jan. 17, 1963)
Published	62 years, 7 months ago (Jan. 17, 1963)
Published Online	28 years, 7 months ago (Jan. 1, 1997)
Published Print	62 years, 7 months ago (Jan. 17, 1963)

Funders 0

None

BibTeX

@article{1963, volume={255}, ISSN={2054-0272}, url={http://dx.doi.org/10.1098/rsta.1963.0002}, DOI={10.1098/rsta.1963.0002}, number={1054}, journal={Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1963}, month=jan, pages={199–215} }

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