Abstract
A simple expression for the angular momentum operator occurring in the theory of the doubly degenerate harmonic oscillator is found. Its action on a radial ket simulates the behavior of the true angular momentum operator, thereby allowing the usual algebras associated with the oscillator to be isomorphic to ones that arise from a purely radial approach. The consequences of these isomorphisms are explored insofar as irreducible tensors are concerned. The matrix elements of the vibrational operators that arise from a purely radial treatment of the oscillator are related to the tensors and evaluated.
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