Turkish Journal of Physics
DOI
10.3906/fiz-1705-11
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
First Page
104
Last Page
115
Recommended Citation
ASHRAFI, SALEH and GOLMANKHANEH, ALI KHALILI
(2018)
"Dimension of quantum mechanical path, chain rule, and extension of Landau's energy straggling method using $F^\alpha$-calculus,"
Turkish Journal of Physics: Vol. 42:
No.
2, Article 2.
https://doi.org/10.3906/fiz-1705-11
Available at:
https://journals.tubitak.gov.tr/physics/vol42/iss2/2
