Riccati Equations as a Scale-Relativistic Gateway to Quantum Mechanics

@article{AlRashid2019RiccatiEA,
  title={Riccati Equations as a Scale-Relativistic Gateway to Quantum Mechanics},
  author={Saeed N. T. Al-Rashid and Mohammed A. Z. Habeeb and Tugdual LeBohec},
  journal={Foundations of Physics},
  year={2019},
  volume={50},
  pages={191-203}
}
Applying the resolution–scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Itô process driven by the solutions of a Riccati equation. We verify that the corresponding Fokker–Planck equation is solved for a probability density corresponding to the squared modulus of the solution of the Schrödinger equation for the same problem. Inspired by the treatment of the one-dimensional case, we… Expand

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