Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Conference Object Citation - WoS: 1Citation - Scopus: 1Exact Quantization of Cauchy-Euler Type Forced Parametric Oscillator(IOP Publishing Ltd., 2016) Atılgan Büyükaşık, Şirin; Çayiç, ZehraDriven 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.Conference Object Citation - WoS: 1Citation - Scopus: 1The Extended Discrete (g'/g)-expansion Method and Its Application To the Relativistic Toda Lattice System(American Institute of Physics, 2009) Aslan, İsmailWe propose the extended discrete (G′/G)-expansion method for directly solving nonlinear differentialdifference equations. For illustration, we choose the relativistic Toda lattice system. We derive further discrete hyperbolic and trigonometric function traveling wave solutions, as well as discrete rational function solutions.