Canonical transformations and accidental degeneracy. I. The anisotropic oscillator

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Abstract
The problem of accidental degeneracy in quantum mechanical systems has fascinated physicists for many decades. The usual approach to it is through the determination of the generators of the Lie algebra responsible for the degeneracy. In these papers we want to focus from the beginning on the symmetry Lie group of canonical transformations in the classical picture. We shall then derive its representation in quantum mechanics. In the present paper we limit our discussion to the anisotropic oscillator in two dimensions, though we indicate possible extensions of the reasoning to other problems in which we have accidental degeneracy.

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