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Fractional Schrödinger equation for heterogeneous media and Lévy like distributions

Author

Listed:
  • Lenzi, E.K.
  • Evangelista, L.R.
  • Zola, R.S.
  • Scarfone, A.M.

Abstract

We investigate an extension of the Schrödinger equation by considering a fractional differential operator for the spatial variable, which simultaneously takes the heterogeneity of the media and Lévy like distributions into account. By using the Green’s function method, we obtain solutions to the equation in the case of the free particle and when it is subject to a delta potential. We also consider a non-local contribution added to the delta potential to explore its influence on the wave function. The solutions show a rich class of spreading behaviors, considerably different from the usual wave function, which may be connected with power-laws and stretched exponential distributions.

Suggested Citation

  • Lenzi, E.K. & Evangelista, L.R. & Zola, R.S. & Scarfone, A.M., 2022. "Fractional Schrödinger equation for heterogeneous media and Lévy like distributions," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007561
    DOI: 10.1016/j.chaos.2022.112564
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    References listed on IDEAS

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    1. Jiang, Xiaoyun & Xu, Mingyu, 2010. "The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3368-3374.
    2. Giovanni Modanese, 2018. "Time in Quantum Mechanics and the Local Non-Conservation of the Probability Current," Mathematics, MDPI, vol. 6(9), pages 1-14, September.
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