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On the direct calculations of the representations of the three-dimensional pure rotation group

Published online by Cambridge University Press:  24 October 2008

Yehiel Lehrer-Ilamed
Yehiel Lehrer-Ilamed
Affiliation:
Israel Atomic Energy Commission, P.O.B. 527, Rehovoth, Israel
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Abstract

Explicit formulae are given for calculating the matrix elements of the irreducible representations of the three-dimensional pure rotation group by the direct method. In addition explicit formulae are derived to calculate the representations of the finite elements of any group when the eigenvalues of the matrix representing the corresponding infinitesimal elements are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 1 , January 1964 , pp. 61 - 66
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Edmonds, A. R.Angular momentum in quantum mechanics (Princeton University Press; Princeton, 1957).CrossRefGoogle Scholar
(2)Fano, U. and Racah, G.Irreducible tensorial sets (Academic Press; New York, 1959).Google Scholar
(3)Wigner, E. P.Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atom- spektren (Vieweg; Braunschweig, 1931).Google Scholar
(4)Wigner, E. P.Group theory and its application to the quantum mechanics of atomic spectra (Academic Press; New York, 1959).Google Scholar
(5)Gel'fand, I. M. and Shapiro, Z. Ya.Representations of the group of rotations of 3-dimensional space and their applications. American Math. Soc. Translations (2), 2 (1956), 207.Google Scholar
(6)Altmann, S. L. and Bradley, C. J.A note on the calculation of the matrix elements of the rotation group. Philos. Trans. Roy. Soc. London, Ser. A, 255 (1962), 193.Google Scholar
(7)Lehrer, Y.On functions of matrices. Bend. Circ. Mat. Palermo (2), 6 (1957), 1.Google Scholar
(8)Wigner, E. P.On matrices which reduce Kronecker products of representations of S.R. groups (unpublished manuscript, 1938).Google Scholar
(9)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcenden al functions (McGraw-Hill; New York, 1955).Google Scholar