University of Guilan Journal of Mathematical Modeling 2345-394X 9 3 2021 09 01 Fractal Kronig-Penney model involving fractal comb potential 331 345 4458 10.22124/jmm.2020.17537.1510 EN Alireza Khalili Golmankhaneh Department of Physics, Urmia Branch Islamic Azad University, Urmia, PO Box 969, Iran Karmina Kamal Ali Department of Mathematics, Faculty of Science, University of Zakho, Iraq Journal Article 2020 09 02 In this article, we suggest a fractal Kronig-Penny model which includes a fractal lattice, a fractal potential energy comb, and a fractal Bloch's theorem on thin Cantor sets. We solve the fractal Schr\"{o}dinger equation for a given potential, using an exact analytical method. We observe that the allowed band energies and forbidden bands in the fractal lattice are bigger than in the standard lattice. These results show the effect of fractal space-time or their fractal geometry  on energy levels. https://jmm.guilan.ac.ir/article_4458_15331da4037abc304165404ab7d73669.pdf