On Fractional Schrödinger Equation

• Autorzy: Rozmej P. , Bandrowski B.
• Konferencja: The Workshop on Current Problems in Physics: Zielona Góra – Lviv, Zielona Góra,19-21 October 2009
• Języki publikacji: EN

Abstrakty

EN

In the note, recent efforts to derive fractional quantum mechanics are recalled. Some applications of a fractional approach to the Schrödinger equation are discussed as well.

Słowa kluczowe

EN

fractional calculus; fractional quantum mechanics; fractional Schrödinger equation

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2010
• Tom: Vol. 16, No. 2
• Strony: 191--194
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Rozmej P.

autor

Bandrowski B.

• Institute of Physics University of Zielona Góra, ul. Szafrana 4a, 65-516 Zielona Góra, Poland,

Bibliografia

• [1] I. Podlubny, Fractional Differential Equations. Academic Press, 1999.
• [2] Fractional Calculus Modeling, http://www.fracalmo.org/
• [3] N. Laskin, Fractional quantum mechanics and Lévy path integrals. Phys. Lett. A 268, 298 (2000); Fractional quantum mechanics. Phys. Rev. E 62, 3135 (2000).
• [4] N. Laskin, Fractional Schrödinger equation. Phys. Rev. E 66, 056108 (2002).
• [5] M. Naber, Time fractional Schrödinger equation. J. Math.Phys. 45, 3339 (2004).
• [6] F. Ben Adda, J. Cresson, Fractional differential equations and the Schrödinger equation. Appl. Math. Comp. 161, 323 (2005).
• [7] R. Herrmann, Properties of fractional derivative Schrödinger type wave equation and a new interpretation of the charmonium spectrum. arXiv:math-ph/05100099 (2006).
• [8] R. Herrmann, The fractional symmetric rigid rotor. J. Phys. G 34, 607 (2007).
• [9] R. Herrmann, q-deformed Lie algebras and fractional calculus. arXiv:0711:3701 (2007).
• [10] R. Herrmann, Gauge invariance in fractional field theories. Phys. Lett. A 372, 5515 (2008).
• [11] R. Herrmann, Fractional dynamic symmetries and the ground properties of nuclei. arXiv:0806.2300 (2008).
• [12] R. Herrmann, Fractional phase transition in medium size metal cluster and some remarks on magic numners in gravitationally and weakly interacting clusters. ArXiv:0907.1953 (2009).
• [13] B. Bandrowski, A. Karczewska, P. Rozmej, Numerical solutions to integral equations equivalent to differential equations with fractional time derivative. Int. J. Appl. Math. Comp. Sci. 20 (2), 261-269 (2010).(http://www.uz.zgora.pl/ prozmej/amcs2.pdf)