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

Abstract

Fα -calculus was recently presented for fractals. We show that the F α -derivative satisfies the chain rule and affirms that the dimension of a quantum mechanical path is two. F α -calculus allows us to extend quantum mechanics to fractal curves. To show the applicability of F α -calculus, we study the fractal model of a particle in a box. F α -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.