Comment on fractality of quantum mechanical energy spectra

Details Comment on fractality of quantum mechanical energy spectra Comment on fractality of quantum mechanical energy spectra

1998-04-21

arxiv.org/abs/chao-dyn/9804034v1

Physics

High Energy Physics

High Energy Physics - Theory

2 pages, LaTeX+RevTeX 3.1

Scientific paper

The fractal properties of the energy spectra of quantum systems are discussed in connection with the paper by S\'aiz and Mart\'inez [Phys. Rev. E 54, 2431 (1996)]. It is shown that for discrete energy levels the Hausdorff--Basicovitch dimension is zero and differs from the Renyi scaling exponents computed by the standard box counting algorithm. The Renyi exponents for the inverse power series data sets (x_n = 1/n^a, n=1,2,...) are computed analytically and they are shown to be d_0 = 1/(1+a) and, as a consequence, d_0 = 1/3 for the Balmer formula.

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