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Time fractional quantum mechanics

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  • Laskin, Nick

Abstract

A time fractional quantum framework has been introduced into quantum mechanics. A new version of the space-time fractional Schrödinger equation has been launched. The introduced space-time fractional Schrödinger equation has a new scale parameter, which is a time fractional generalization of Planck’s constant in quantum physics.

Suggested Citation

  • Laskin, Nick, 2017. "Time fractional quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 16-28.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:16-28
    DOI: 10.1016/j.chaos.2017.04.010
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    Citations

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    Cited by:

    1. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    2. Benjemaa, Mondher, 2018. "Taylor’s formula involving generalized fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 182-195.
    3. Borin, Daniel, 2024. "Caputo fractional standard map: Scaling invariance analyses," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. Wei, Dongmei & Liu, Hailing & Li, Yongmei & Gao, Fei & Qin, Sujuan & Wen, Qiaoyan, 2023. "Quantum speed limit for time-fractional open systems," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    5. Al-khedhairi, A. & Matouk, A.E. & Khan, I., 2019. "Chaotic dynamics and chaos control for the fractional-order geomagnetic field model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 390-401.
    6. 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).
    7. Zu, Chuanjin & Yu, Xiangyang, 2022. "Time fractional Schrödinger equation with a limit based fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    8. Iomin, Alexander, 2023. "Fractional Floquet theory," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    9. Wei, Dongmei & Liu, Hailing & Li, Yongmei & Wan, Linchun & Qin, Sujuan & Wen, Qiaoyan & Gao, Fei, 2024. "Non-Markovian dynamics of time-fractional open quantum systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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