About Schrödinger Equation on Fractals Curves Imbedding in R 3

Khalili Golmankhaneh A., Golmankhaneh A. K., Baleanu D.

International Journal of Theoretical Physics, vol.54, no.4, pp.1275-1282, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.1007/s10773-014-2325-0
  • Journal Name: International Journal of Theoretical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1275-1282
  • Keywords: Feynman path, Fractal calculus, Fractal quantum mechanics, Schrëdinger fractional equation
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper we introduced the quantum mechanics on fractal time-space. In a suggested formalism the time and space vary on Cantor-set and Von-Koch curve, respectively. Using Feynman path method in quantum mechanics and Fα-calculus we find Schrëdinger equation on on fractal time-space. The Hamiltonian and momentum fractal operator has been indicated. More, the continuity equation and the probability density is given in view of Fα-calculus.