Dimension of quantum mechanical path, chain rule, and extension of Landau's energy straggling method using $F^\alpha$-calculus

Authors: SALEH ASHRAFI, ALI KHALILI GOLMANKHANEH

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

Keywords: $F^{\alpha}$-calculus, fractal quantum paths, staircase function, energy straggling

Full Text: PDF