Notation for the wave functions for (a) scattering with interface of the piecewise constant potential among the values and and (b) the propagation through each constant potential .
First steps of development of (a) triadic and (b) polyadic, , symmetrical generalized Cantor sets. Black and white regions denote the potential values and , respectively. The right plot also shows the definition of the scale factor and the lacunarity parameter characterizing polyadic Cantor sets.
Potential wells for (a), (b), and (c) for a polyadic Cantor set potential with and .
Scattering reflection coefficient for the polyadic Cantor prefractal potentials with (a) and (b) with , , and .
Twist plots, that is, gray-scale representation of the scattering reflection coefficient (in decibels) as a function of the normalized energy and the lacunarity parameter for the polyadic Cantor prefractal potentials with (a) and (b) , for , , and .
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