Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-08T21:27:37.141Z Has data issue: false hasContentIssue false
  • English
  • Français

Some properties of Wigner coefficients and hyperspherical harmonics

Published online by Cambridge University Press:  24 October 2008

A. P. Stone
A. P. Stone
Affiliation:
Clarendon LaboratoryOxford
Get access Rights & Permissions [Opens in a new window]

Abstract

General shift operators for angular momentum are obtained and applied to find closed expressions for some Wigner coefficients occurring in a transformation between two equivalent representations of the four-dimensional rotation group. The transformation gives rise to analytical relations between hyperspherical harmonics in a four-dimensional Euclidean space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 3 , July 1956 , pp. 424 - 430
Copyright
Copyright © Cambridge Philosophical Society 1956

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bateman, H.Proc. Lond. math. Soc. (2) 3 (1905), 111.CrossRefGoogle Scholar
(2)Condon, E. U. and Shortley, G. H.The theory of atomic spectra (Cambridge, 1935), chap. 3.Google Scholar
(3)Corson, E. M.Perturbation methods in the quantum mechanics of n-electron systems (London, 1951), chap. 3, §§21, 22.Google Scholar
(4)Hill, M. J. M.Trans. Camb. phil. Soc. 13 (1883), 273.Google Scholar
(5)Hobson, E. W.Proc. Lond. math. Soc. (1) 25 (1894), 49.Google Scholar
(6)Simon, A.Numerical table of the Clebsch-Gordon coefficients (Oak Ridge National Laboratory report 1718, 1954).Google Scholar
(7)Thomas, L. H.Ann. Math., Princeton, 42 (1941), 113.CrossRefGoogle Scholar
(8)Wigner, E. P.Gruppentheorie (Braunschweig, 1931), p. 206.Google Scholar