Atılgan Büyükaşık, ŞirinÇayiç, Zehra2017-07-262017-07-262016Atılgan Büyükaşık, Ş., and Çayiç, Z. (2016). Exact quantization of Cauchy-Euler type forced parametric oscillator. Journal of Physics: Conference Series, 766(1). doi:10.1088/1742-6596/766/1/0120031742-65881742-6596http://doi.org/10.1088/1742-6596/766/1/012003http://hdl.handle.net/11147/6024International Conference on Quantum Science and Applications, ICQSA 2016; Eskisehir Osmangazi University Congress and Culture CentreEskisehir; Turkey; 25 May 2016 through 27 May 2016Driven 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.eninfo:eu-repo/semantics/openAccessDifferential equationsParametric oscillatorsAlgebraic approachesProbability densitiesQuantum oscillatorsConference Object2-s2.0-8499590047810.1088/1742-6596/766/1/01200310.1088/1742-6596/766/1/012003