Dimension of quantum mechanical path, chain rule, and extension of Landau’s energy straggling method using F α -calculus

Abstract

FαFα-calculus was recently presented for fractals. We show that the FαFα-derivative satisfies the chain rule and affirms that the dimension of a quantum mechanical path is two. FαFα-calculus allows us to extend quantum mechanics to fractal curves. To show the applicability of FαFα-calculus, we study the fractal model of a particle in a box. FαFα-calculus is suitable for describing the motion of particles with a fractal route through matter. In addition, we extend Landau's energy straggling method of charged particles to fractals.