English

Schr\"odinger Equation on Fractals Curves Imbedding in $R^3$

Mathematical Physics 2014-09-05 v2 math.MP

Abstract

In this paper we have generalized the quantum mechanics on fractal time-space. The time is changing on Cantor-set like but space is considered as fractal curve like Von-Koch curve. The Feynman path method in quantum mechanics has been suggested on fractal curve. Using FαF^{\alpha}-calculus and Feynman path method we found the Schr\"{e}dinger on fractal time-space. The Hamiltonian operator and momentum operator has been derived. More, the continuity equation and the probability density is given in generalized formulation.

Keywords

Cite

@article{arxiv.1308.0291,
  title  = {Schr\"odinger Equation on Fractals Curves Imbedding in $R^3$},
  author = {Alireza Khalili Golmankhaneh and Dumitru Baleanu},
  journal= {arXiv preprint arXiv:1308.0291},
  year   = {2014}
}