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We study the scattering problem at generalized Cantor-like potentials characterized by the expansion rate a and duplication number N, and derive an exact formula of transmittance. It was found that the transmittance is expressed with Chebyshev polynomials of the second kind, and the multifractality of the reflectance varies depending on a and N.
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Ogawana et al. (2018) studied this question.
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