It was shown that the Lindemann ratio (L) can be calculated by means of the delocalized criterion of melting for classical crystals, i. e. those with a melting point (T_m) greater than the Debye temperature (Theta): T_m/Theta>1.5. It was shown that for classical single-component crystals, the L value is determined only by the crystal structure. Calculations for various structures of classical crystals showed good agreement with the estimates of other authors. A generalization of the Lindemann relation was obtained for the case of quantum single-component crystals, i. e. for which T_m/Theta<0.4. It was shown that for quantum crystals, the Lindemann ratio is determined not only by the crystal structure, but also by the function Theta/T_m. Therefore, when moving from the classical to the quantum domain, the T_m(Theta) function changes its functional dependence. It was shown that for quantum crystals, the L value decreases with increasing pressure along the melting line. For quantum nanocrystals, the L value increases with an isobaric decrease in the size of the nanocrystal. At the same time, the more noticeably the shape of the quantum nanocrystal deviates from the energy-optimal shape, the greater the sized increase in the Lindemann ratio. A generalization of the delocalized criterion of melting was obtained for the case of quantum single-component crystals. Keywords: melting, delocalization, Debye temperature, quantum crystal, nanocrystal, hydrogen, helium.

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