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Time fractional Schrödinger equation with a limit based fractional derivative

Author

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  • Zu, Chuanjin
  • Yu, Xiangyang

Abstract

We re-examine the time fractional Schrödinger equation. The effects of different fractional derivatives and different treatments of imaginary unit i on the time fractional Schrödinger equation are studied. Considering the physical meaning of imaginary unit i in the standard Schrödinger equation, we believe that fractional order of imaginary unit i is inappropriate, which is proved by the evolution of a free particle. Meanwhile, comparing with the Caputo fractional derivative with many restrictions, time fractional Schrödinger equation with a limit based fractional derivative is more in line with the existing physical world. Our results might provide a new perspective to understand the time fractional Schrödinger equation.

Suggested Citation

  • Zu, Chuanjin & Yu, Xiangyang, 2022. "Time fractional Schrödinger equation with a limit based fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001515
    DOI: 10.1016/j.chaos.2022.111941
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    References listed on IDEAS

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    1. B. N. Narahari Achar & Bradley T. Yale & John W. Hanneken, 2013. "Time Fractional Schrodinger Equation Revisited," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-11, July.
    2. Zu, Chuanjin & Gao, Yanming & Yu, Xiangyang, 2021. "Time fractional evolution of a single quantum state and entangled state," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Laskin, Nick, 2017. "Time fractional quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 16-28.
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