Fractal kronig-penney model involving fractal comb potential

Khalili Golmankhaneh A., Ali K. K.

Journal of Mathematical Modeling, cilt.9, sa.3, ss.331-345, 2021 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.22124/jmm.2020.17537.1510
  • Dergi Adı: Journal of Mathematical Modeling
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.331-345
  • Anahtar Kelimeler: 35J10, Fractal calculus, Fractal lattice. AMS Subject Classification 2010: 28A80, Fractal Schrödinger equation, Local fractal derivative
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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 Schrödinger 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.