Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/6839
Title: Exactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators
Authors: Atılgan Büyükaşık, Şirin
Çayiç, Zehra
Keywords: Quantization
Quantum parametric oscillators
Oscillators
Issue Date: Dec-2016
Publisher: American Institute of Physics
Source: Atılgan Büyükaşık, Ş., and Çayiç, Z. (2016). Exactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators. Journal of Mathematical Physics, 57(12). doi:10.1063/1.4972293
Abstract: We introduce exactly solvable quantum parametric oscillators, which are generalizations of the quantum problems related with the classical orthogonal polynomials of Hermite, Laguerre, and Jacobi type, introduced in the work of Büyükaşık et al. [J. Math. Phys. 50, 072102 (2009)]. Quantization of these models with specific damping, frequency, and external forces is obtained using the Wei-Norman Lie algebraic approach. This determines the evolution operator exactly in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time-evolution of wave functions and coherent states are found explicitly. Probability densities, expectation values, and uncertainty relations are evaluated and their properties are investigated under the influence of the external terms.
URI: https://doi.org/10.1063/1.4972293
http://hdl.handle.net/11147/6839
ISSN: 0022-2488
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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