We analyze the reconstruction by Wu and Sprung [Phys. Rev. E 48, 2595 (1993)] of a fractal one-dimensional potential, the quantum spectrum of which reproduces the first 500 nontrivial zeros of the Riemann {ζ} function. Our construction is based on a spectrum with Gaussian unitary ensemble statistics as far as the nearest-neighbor spacing distribution is concerned. Our results show that a reliable estimate of the fractal dimension of the potential necessitates a very large number of levels.
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Ramani et al. (1995) studied this question.
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