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arXiv · 1308.0291

Schrödinger Equation on Fractals Curves Imbedding in $R^3$

Alireza Khalili Golmankhaneh·Dumitru Baleanu
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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 $F^α$-calculus and Feynman path method we found the Schrëdinger 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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Alireza Khalili Golmankhaneh, Dumitru Baleanu. 2013-10-12. Schrödinger Equation on Fractals Curves Imbedding in $R^3$. https://doi.org/10.1016/s0550-3213(01)00405-9.

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