Fractional-time Schrödinger equation: Fractional dynamics on a comb

@article{Iomin2011FractionaltimeSE,
  title={Fractional-time Schr{\"o}dinger equation: Fractional dynamics on a comb},
  author={Alexander Iomin},
  journal={Chaos Solitons \& Fractals},
  year={2011},
  volume={44},
  pages={348-352}
}
  • A. Iomin
  • Published 1 May 2011
  • Mathematics, Physics
  • Chaos Solitons & Fractals
The physical relevance of the fractional time derivative in quantum mechanics is discussed. It is shown that the introduction of the fractional time Schrodinger equation (FTSE) in quantum mechanics by analogy with the fractional diffusion ∂∂t→∂α∂tα can lead to an essential deficiency in the quantum mechanical description, and needs special care. To shed light on this situation, a quantum comb model is introduced. It is shown that for α = 1/2, the FTSE is a particular case of the quantum comb… 
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