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Colegrave, R. K.; Mannan, M. A.

Invariants for the time-dependent harmonic oscillator. (English) Zbl 0658.70020

J. Math. Phys. 29, No. 7, 1580-1587 (1988).
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.

Cited in 4 Documents

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.)

Keywords:

invariants for the damped oscillator; anisotropic oscillator; canonical transformation
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\textit{R. K. Colegrave} and \textit{M. A. Mannan}, J. Math. Phys. 29, No. 7, 1580--1587 (1988; Zbl 0658.70020)
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References:

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