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Representations of the n-dimensional rotation group

Published online by Cambridge University Press:  24 October 2008

A. P. Stone
A. P. Stone
Affiliation:
Department of MathematicsUniversity of Hull
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Abstract

The commutators of the infinitesimal operators of the n-dimensional rotation group Rn with vector operators under Rn are expressed in a vectorial notation. The infinitesimal operators for the representations (l 0…0) are treated in detail. Shift operators for l are constructed and are used to derive the branching rule for these representations. The energy levels and degeneracy of bound states of a particle under an inverse square force in n dimensions are found by wave mechanics and by expressing the Hamiltonian in terms of Casimir's operator for Rn+1. Differential operators which transform one radial wave function into another are obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 469 - 475
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Boerner, H.Darstellungen von Gruppen (Berlin, 1955).CrossRefGoogle Scholar
(2)Casimir, H. K.Nederlandse Akad. Wetensch. Proc. Ser. A, 34 (1931), 844.Google Scholar
(3)Dirac, P. A. M.The principles of quantum mechanics, 3rd ed. (Oxford, 1947).Google Scholar
(4)Güttinger, P. and Pauli, W. Z.Physik. 67 (1931), 743.CrossRefGoogle Scholar
(5)Jackson, T. A. S.Proc. Phys. Soc. A, 66 (1953), 958.CrossRefGoogle Scholar
(6)Milne, E. A.Vectorial mechanics (London, 1948).Google Scholar
(7)Murnaghan, F. D.The theory of group representations (Baltimore, 1938).Google Scholar
(8)Racah, G.Phys. Rev. 63 (1943), 367.CrossRefGoogle Scholar
(9)Stone, A. P.Proc. Camb. Phil. Soc. 52 (1956), 424.CrossRefGoogle Scholar
(10)Stone, A. P.Proc. Camb. Phil. Soc. 57 (1961), 460.CrossRefGoogle Scholar
(11)Weyl, H.The classical groups (Princeton, 1946).Google Scholar