Mapping of classical canonical transformations to quantum unitary operators

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Abstract
Classical linear transformations in coordinate-momentum phase space are mapped to unitary quantum-mechanical operators in Hilbert space to produce a generalization of squeeze operators. The classical to quantum transition is manifestly apparent in the derivation. The unitary operators are evaluated in the coherent-state representation using the ‘‘integration within ordered products’’ technique in the one- and two-mode cases. Application of these operators results in a new generalization of coherent states.

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