Classical and Quantum Action-Phase Variables for Time-Dependent Oscillators
arXiv:quant-ph/0101076 · doi:10.1103/PhysRevA.64.012104
Abstract
For a time-dependent classical quadratic oscillator we introduce pairs of real and complex invariants that are linear in position and momentum. Each pair of invariants realize explicitly a canonical transformation from the phase space to the invariant space, in which the action-phase variables are defined. We find the action operator for the time-dependent oscillator via the classical-quantum correspondence. Candidate phase operators conjugate to the action operator are discussed, but no satisfactory ones are found.
RevTex 15 pages, no figure; appendices and references added
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