  It is shown that the rate of corrections to the hydrogen atom and harmonic
oscillator due to profound quantum-gravitational effect of space-time dimension
running/reduction coincides well with those obtained by means of the
minimum-length deformed quantum mechanics. The rate of corrections are pretty
much the same within the accuracy by which we can judge the
quantum-gravitational corrections at all. Such a convergence of results makes
the concept of space-time dimension running more appreciable. As a remarkable
distinction, the energy shift due to dimension reduction has the opposite sign
as compared with the correction obtained by means of the minimum-length
modified quantum mechanics. Thereby, the sign of total quantum-gravitational
correction remains obscure.
