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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.

MSC:

70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
70J99 Linear vibration theory
81Q99 General mathematical topics and methods in quantum theory
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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