Browsing Mathematics / Matematik by Author "Atılgan Büyükaşık, Şirin"
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Damped parametric oscillator and exactly solvable complex Burgers equations
Atılgan Büyükaşık, Şirin; Pashaev, Oktay (IOP Publishing, 2012)We obtain exact solutions of a parametric Madelung fluid model with dissipation which is linearazible in the form of Schrödinger equation with time variable coefficients. The corresponding complex Burgers equation is solved ... 
Exact quantization of CauchyEuler type forced parametric oscillator
Atılgan Büyükaşık, Şirin; Çayiç, Zehra (IOP Publishing, 201610)Driven and damped parametric quantum oscillator is solved by WeiNorman Lie algebraic approach, which gives the exact form of the evolution operator. This allows us to obtain explicitly the probability densities, timeevolution ... 
Exact solutions of forced Burgers equations with time variable coefficients
Atılgan Büyükaşık, Şirin; Pashaev, Oktay (Elsevier, 201307)In this paper, we consider a forced Burgers equation with time variable coefficients of the form Ut+(μ̇(t)/μ(t))U+UUx=(1/2μ(t))Uxxω2(t)x, and obtain an explicit solution of the general initial value problem in terms of a ... 
Exactly solvable Hermite, Laguerre, and Jacobi type quantum parametric oscillators
Atılgan Büyükaşık, Şirin; Çayiç, Zehra (American Institute of Physics, 201612)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 ... 
Exactly solvable Madelung fluid and complex Burgers equations: A quantum SturmLiouville connection
Atılgan Büyükaşık, Şirin; Pashaev, Oktay (Springer, 201211)Quantum SturmLiouville problems introduced in our paper (Büyükaşi{dotless}k et al. in J Math Phys 50:072102, 2009) provide a reach set of exactly solvable quantum damped parametric oscillator models. Based on these results, ... 
Exactly solvable quantum SturmLiouville problems
Atılgan Büyükaşık, Şirin; Pashaev, Oktay; Tığrak Ulaş, Esra (American Institute of Physics Publising, 2009)The harmonic oscillator with timedependent parameters covers a broad spectrum of physical problems from quantum transport, quantum optics, and quantum information to cosmology. Several methods have been developed to ... 
Madelung representation of damped parametric quantum oscillator and exactly solvable SchrödingerBurgers equations
Atılgan Büyükaşık, Şirin; Pashaev, Oktay (American Institute of Physics Publishing, 20101201)We construct a Madelung fluid model with time variable parameters as a dissipative quantum fluid and linearize it in terms of Schrödinger equation with timedependent parameters. It allows us to find exact solutions of the ...