We elucidate the relationship between the linear oscillator with time-dependent frequency, damping, and driving, and the autonomous oscillator with unit frequency and no damping or driving. Such a relationship can be derived from a canonical transformation and a redefinition of the time. A study of the scalars of the transformation makes it possible to write down the evolving quantum states for the nonautonomous Hamiltonian given the evolving states for the autonomous harmonic oscillator.
Reduction method for the linear quantum or classical oscillator with time-dependent frequency, damping, and driving
Degli Esposti Boschi;
2000
Abstract
We elucidate the relationship between the linear oscillator with time-dependent frequency, damping, and driving, and the autonomous oscillator with unit frequency and no damping or driving. Such a relationship can be derived from a canonical transformation and a redefinition of the time. A study of the scalars of the transformation makes it possible to write down the evolving quantum states for the nonautonomous Hamiltonian given the evolving states for the autonomous harmonic oscillator.File in questo prodotto:
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