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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

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