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 -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}
}