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arXiv:1601.00727 · Annals of Physics

Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator

Lin Zhang, Weiping Zhang

Published Jul 29, 2016• 10 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2016.07.032

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Driven and damped parametric quantum oscillator is solved by Wei-Norman Lie algebraic approach, which gives the exact form of the evolution operator. This allows us to obtain explicitly the probability densities, time-evolution of initially Glauber coherent states, expectation values and uncertainty relations. Then, as an exactly solvable model, we introduce the driven Cauchy-Euler type quantum parametric oscillator, which appears as self-adjoint quantization of the classical Cauchy-Euler differential equation. We discuss some typical behavior of this oscillator under the influence of external terms and give a concrete example.