Quantum-gravitational corrections to the hydrogen atom and harmonic oscillator

Abstract

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.

8 pages

References in corpus (8)

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Cited by in corpus (3)

• Note on the Existence of Hydrogen Atoms in Higher Dimensional Euclidean Spaces
• The quantum N-body problem with a minimal length
• Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\ge 4$?