Classical and quantum action-phase variables for time-dependent oscillators - art. no. 012104

For a time-dependent classical quadratic oscillator we introduce pairs of r eal and complex invariants that are linear in position and momentum. Each p air of invariants realize explicitly a canonical transformation from the ph ase space to the invariant space, in which the action-phase variables are d efined. We find the action operator for the time-dependent quantum oscillat or via the classical-quantum correspondence. Candidate phase operators conj ugate to the action operator are discussed, but no satisfactory ones are fo und.