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Effects of the medium fractionality and oscillating potential profiles on the Superarrivals of the Gaussian wave packets

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  • Tehrani, D. Haji Taghi
  • Solaimani, M.

Abstract

So far, the less studied superarrival concept is only investigated in the standard integer-order Schrodinger equation formalism. In this research, we assume a fractional Schrodinger equation. Also, in the available papers on the superarrival phenomenon, a monotonic increasing or decreasing potential profile is considered, while here, an oscillating potential profile is supposed. A Gaussian wave packet impinging on an oscillating potential profile has been explored. It is shown that the wave packet velocity changes according to relation α/2 kα-1 = v, assuming ћ = 1and m = 1. The wave packet traveling speed slows down using the fractionality order α. Also, we have demonstrated that the fractionality order α can be used as a tuning tool to obtain atypical early arrival magnitude η. Finally, we propose that the superarrival concept can be experimentally tested by impinging a Gaussian wave packet on an oscillating potential profile that can be realized in the tautomerization and isomerization reactions.

Suggested Citation

  • Tehrani, D. Haji Taghi & Solaimani, M., 2023. "Effects of the medium fractionality and oscillating potential profiles on the Superarrivals of the Gaussian wave packets," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000395
    DOI: 10.1016/j.chaos.2023.113138
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    References listed on IDEAS

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    1. Özkan Güner & Dursun Eser, 2014. "Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-8, July.
    2. Jamshir, Narges & Lari, Behzad & Hassanabadi, Hassan, 2021. "The time independent fractional Schrödinger equation with position-dependent mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. Tare, Jeffrey D. & Esguerra, Jose Perico H., 2014. "Transmission through locally periodic potentials in space-fractional quantum mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 43-53.
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