Quantum tunneling from family of Cantor potentials in fractional quantum mechanics

• URL: http://arxiv.org/abs/2301.00674v1
• Date: Thu, 29 Dec 2022 06:36:13 GMT
• Title: Quantum tunneling from family of Cantor potentials in fractional quantum mechanics
• Authors: Vibhav Narayan Singh, Mohammad Umar, Mohammad Hasan, Bhabani Prasad Mandal
• Abstract summary: We consider two types of potentials: general Cantor and general Smith-Volterra-Cantor potential. The present study brings for the first time, the study of quantum tunneling through fractal potential in fractional quantum mechanics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explore the features of non-relativistic quantum tunneling in space fractional quantum mechanics through a family of Cantor potentials. We consider two types of potentials: general Cantor and general Smith-Volterra-Cantor potential. The Cantor potential is an example of fractal potential while the Smith-Volterra-Cantor potential doesn't belong to the category of a fractal system. The present study brings for the first time, the study of quantum tunneling through fractal potential in fractional quantum mechanics. We report several new features of scattering in the domain of space fractional quantum mechanics including the emergence of energy-band like features from these systems and extremely sharp transmission features. Further the scaling relation of the scattering amplitude with wave vector $k$ is presented analytically for both types of potentials.

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