Sunday, August 4, 2013

1308.0291 (Alireza Khalili Golmankhaneh et al.)

Schrödinger Equation on Fractals Curves Imbedding in $R^3$    [PDF]

Alireza Khalili Golmankhaneh, Ali Khalili Golmankhaneh, Dumitru Baleanu
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 $F^{\alpha}$-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.
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