Abstract
We discuss through the examples of the oscillator with centrifugal potential and the Coulomb problem in dilated form, the general procedure for finding the representation in quantum mechanics of non-linear and non-bijective canonical transformations. The ambiguity group associated with the canonical transformations and the irreducible representations of this group, which lead to the concept of ambiguity spin, suggest also that some features of the spectra of quantum operators are already present in the classical picture.
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