Fractal Kronig-Penney model involving fractal comb potential

Abstract. 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¨odinger 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.