STUDY BROWNIAN MOTION AND SHOWING THE TRAJECTORIES OF PARTICLES USING FRACTAL GEOMETRY.

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