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Invariants for the time-dependent harmonic oscillator. (English) Zbl 0658.70020
A systematic method is presented for the construction of invariants for the damped oscillator under the action of a driving force and for the N- dimensional isotropic or anisotropic oscillator. Invariants for time- dependent oscillators are obtained by canonical transformation. The treatment holds in both classical and quantum mechanics.

70H15Canonical and symplectic transformations in particle mechanics
70J99Linear vibration theory
81Q99General mathematical topics and methods in quantum theory
37J35Completely integrable systems, topological structure of phase space, integration methods
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
Full Text: DOI
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