Document Type : Research Paper
Author
Department of physics, College of Education, University of Anbar
Abstract
In the present work, trajectories of particle in an infinite square well, finite square well, with simple harmonic oscillators and double well potentials are shown and fractal dimension of these trajectories is calculated. The fractal dimension to theses trajectories is found close to 1.5 which is fractal dimension of fractional Brownian motion. Here, to show that, one can modify Hermann and Al-Rashid approaches in direct applications of Scale Relativity Theory.
Keywords
Main Subjects
[1] E. Nelson," Dynamical Theories of Brownian Motion", Princeton, N.J.: Princeton
University Press, 1967.
[2] B. Mandelbrot and J. W. Van Ness," Fractional Brownian motions, fractional noises and applications ", SIAM Review, 10, 422-437, 1968.
[3] H. P. McKean, Jr. and D. Sullivan, "Brownian motion and harmonic functions on the class surface of the thrice-punctured sphere", Adv. In Math., 51:203{211, 1984.
[4] S. J. Lin, "Stochastic analysis of fractional Brownian motions", Stochastics andStochastics Reports, 55, 121-140, 1995.
[5] E. E. Peters. Chaos and Order in the Capital Markets. John Wiley and Sons, Inc., New York, 1991.
[6] P. S. Addison,"Fractals and Chaos: An Illustrated Course ", Institute of Physics Publishing, Bristol, 1997.
[7] R. P. Hermann, "Numerical Simulation of a Quantum Patrical in a Box", J. Phys. A; Math. Gen. 30, pp.3967-3975, 1997.
[8] L. Nottale, "Fractal Space-Time and Microphysics: To wards of a Theory of Scale Relativity", World Scientific, (First Reprint) 1998.
[9] B. Mandelbrot, "Fractal Geometry: What is it, and What Does It Do?", Proc. R. Soc., Vol. 423, No. 1864. London, pp. 3-16, 1989.
[10] B. Mandelbrot, "The Fractal Geometry of Nature", W. H. Freeman and Company, 1983.
[11] F. Barnsley and A. D. Sloan. "A Better Way to Compress Images", Byte, pp. 215-223, 1988.
[12] P. P. Alex. "Fractal Based Description of Natural Scenes", Trans. on Pattern Analysis and Machine Intelligence, Vol. Pami-6, No.6, pp. 661-674, 1984.
[13] M. F. Barnsley, "Fractals Everywhere", 2nd Ed., Acad. Press Professional, 1988
[14] D. M. Davis, "The Nature and Power of Mathematics", Princeton Univ. Press, 1993.
[15] S. N. T. Al-Rashid "Some Applications of Scale Relativity Theory in Quantum Physics", Ph.D Thesis, College of Science, Al-Mustansiriyah University, 2006.
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