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Fractal Kronig-Penney model involving fractal comb potential | ||
| Journal of Mathematical Modeling | ||
| مقاله 1، دوره 9، شماره 3، آذر 2021، صفحه 331-345 اصل مقاله (821.87 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2020.17537.1510 | ||
| نویسندگان | ||
| Alireza Khalili Golmankhaneh* 1؛ Karmina Kamal Ali2 | ||
| 1Department of Physics, Urmia Branch Islamic Azad University, Urmia, PO Box 969, Iran | ||
| 2Department of Mathematics, Faculty of Science, University of Zakho, Iraq | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Fractal calculus؛ fractal Schrodinger equation؛ local fractal derivative؛ fractal lattice | ||
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