Sequences of point transformations and linear canonical transformations in classical and quantum mechanics

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Abstract
Sequences of point transformations and canonical linear transformations are considered in classical and quantum mechanics. It is shown that the unitary representations of such transformations can be obtained, in general, in the sense that in the limit, classical behavior is retrieved. In the particular case of one point transformation combined with two linear transformations, the results found in this way are exact. A new class of differential equations is thereby solved by quadratures.