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Classical and Quantum Action-Phase Variables for Time-Dependent Oscillators

Sang Pyo Kim·Don N. Page
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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.

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Sang Pyo Kim, Don N. Page. 2001-03-07. Classical and Quantum Action-Phase Variables for Time-Dependent Oscillators. https://doi.org/10.1103/physreva.64.012104

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