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Won Sang Chung

Publications and source records attributed to Won Sang Chung.

27 records · Page 2Linked to original sources
arXiv2013

New $q-$Hermite polynomials: characterization, operator algebra and associated coherent states

This paper addresses a construction of new $q-$Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self-adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem.

math-ph↗
arXiv2013

On the q-analogue of Laplace transform

In this paper, we consider a q-analogue of Laplace transform and we investigate some properties of q-Laplace transform. From our investigation, we derive some interesting formulae related to q-Laplace transform.

math.NT↗
arXiv2013

On the fractional damped oscillators and fractional forced oscillators

In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $ν$. We deal with the motion of a body in a resisting medium where the retarding force is assumed to be proportional to the fractional velocity which is obtained by acting the fractional derivative on the position. The fractional harmonic oscillator problem, fractional damped oscillator problem and fractional forced oscillator problem are also studied.

physics.gen-ph↗
arXiv2012

On the representation of $A_{\kk}(2)$ algebra and $A_{\kk}(d)$ algebra

In this paper the representation of $A_{\kk}(2)$ algebra given by Daoud and Kibler [M.Daoud and M.Kibler, J.Phys.A 43 115303 (2010), 45 244036 (2012)] is investigated. It is shown that the new generators are necessary for consistency of the algebra. The multi-mode extension of $A_{\kk}(2)$ algebra, which is called $A_{\kk}(d)$ algebra, is also obtained. The positivity condition of the energy spectrum is also investigated for $A_{\kk}(2)$ algebra and $A_{\kk}(d)$ algebra.

math-ph↗
arXiv2012

Study on the mechanical system related to Hahn's discrete time derivative

In this paper, we use the quantum variational calculus related to Hahn's discrete time derivative construct the deformed version for the classical mechanics related to the Hahn's calculus. We deal with the deformed dynamics such as the motion with constant velocity and the motion with constant acceleration. Moreover, we extend our work to the motion of a body in a resisting medium by using the new identity for an infinite ($q,w$)-series, where the retarding force is assumed to be proportional to the deformed average velocity.

math-ph↗