Now showing items 1-6 of 6

• #### Exact quantization of Cauchy-Euler type forced parametric oscillator ﻿

(IOP Publishing, 2016-10)
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 ...
• #### Exact solutions of forced Burgers equations with time variable coefficients ﻿

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))Uxx-ω2(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 ﻿

(American Institute of Physics, 2016-12)
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 Sturm-Liouville connection ﻿

Quantum Sturm-Liouville 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 Sturm-Liouville problems ﻿

(American Institute of Physics Publising, 2009)
The harmonic oscillator with time-dependent 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 Schrödinger-Burgers equations ﻿

(American Institute of Physics Publishing, 2010-12-01)
We construct a Madelung fluid model with time variable parameters as a dissipative quantum fluid and linearize it in terms of Schrödinger equation with time-dependent parameters. It allows us to find exact solutions of the ...
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