Exact quantization of Cauchy-Euler type forced parametric oscillator

International Conference on Quantum Science and Applications 2016

Büyükaik, Sirin A.^1 ; Çayiç, Zehra^1

Department of Mathematics, Izmir Institute of Technology, Gulbahce Campus, Urla, Izmir

35430, Turkey^1

关键词: Algebraic approaches;    Evolution operator;    Exactly solvable model;    Expectation values;    Probability densities;    Quantum oscillators;    Time evolutions;    Uncertainty relation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/766/1/012003/pdf
DOI  :  10.1088/1742-6596/766/1/012003

来源: IOP

【 摘 要 】

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.