The Wigner-Dunkl-Newton mechanics with time-reversal symmetry

W. Sang Chung, H. Hassanabadi


In this paper we use the Dunkl derivative with respect to time to construct the
Wigner-Dunkl-Newton mechanics with time-reversal symmetry. We deflne the WignerDunkl-Newton velocity and Wigner-Dunkl-Newton acceleration and construct the WignerDunkl-Newton equation of motion. We also discuss the Hamiltonian formalism in the
Wigner-Dunkl-Newton mechanics. We discuss some deformed elementary functions such
as the ”-deformed exponential functions, ”-deformed hyperbolic functions and ”-deformed
trigonometric functions. Using these we solve some problems in on dimensional WignerDunkl-Newton mechanics mechanics.


Dunkl derivative, Wigner-Dunkl-Newton mechanics, time-reversal symmetry.

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F. Jackson, Proc. Edinburgh Math. Soc. 22 (1904) 28.

F. Jackson, On q-functions and a certain difierence operator. Trans. Roy Soc. Edinburgh

(1908) 253.

A. Lavagno, A.Scarfone and P. Swamy, Eur.Phys.J.C47 (2006) 253.

P. Caban, A. Dobrosielski, A. Krajewska and Z. Walczak , Phys.Lett. B327 (1994) 287.

S. Samko, A. Kilbas and O.Marichev, Fractional Integrals and Derivatives ( Gordon and

Breach, New York, 1993).

K.Miller and B.Ross, An Introduction to the Fractional Calculus and Fractional Difierential Equations ( Wiley, New York, 1993).

[7] A.Kilbas, H.Strivatava and J.Trujillo, Theory and Application of Fractional Difierential

Equations ( Wiley, New York, 1993).

I.Pdolubny, Fractional Difierential Equations (Academic Press,New York, 1999).

K.Oldham and J.spanier, The fractional Calculus ( Academic Press, New York, 1974).

R. Khalil,M. Al Horani, A. Yousef and M. Sababheh, J. Comput. Appl. Math. 264,


M.Klimek , Czechoslovak Journal of Physics 55 (2005) 1447.

F. Riewe, Phys. Rev. E 55 (1997) 3581.

W. Chung, Journal of Computational and Applied Mathematics 290, 150 (2015).

W. Chung and H.Hassanabadi, Int. J.Theor.Phys 56, 851 (2017).

W. Chung and H.Hassanabadi, One dimensional quantum mechanics with Dunkl derivative (2018).

W. Chung, E.Jang and S.Park, Journal of the Korean Physical Society 68, 379 (2016).



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Revista Mexicana de Física

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