  In this paper, we compare the RMF theory and the model of deformed oscillator
shells (DOS) in description of the quantum properties of the bound states of
the spherically symmetric light nuclei. We obtain an explicit analytical
relation between differential equations for the RMF theory and DOS model, which
determine wave functions for nucleons. On such a basis we perform analysis of
correspondence of quantum properties of nuclei. We find: (1) Potential
$V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$
with joint part $h$ coincident exactly with the nucleon wave function of DOS
model with potential $V_{\rm shell}$. But, a difference between $V_{RMF}$ and
$V_{\rm shell}$ is essential for any nucleus. (2) The nucleon wave functions
and densities obtained by the DOS and RMF theories are essentially different.
The nucleon densities of the RMF theory contradict to knowledge about
distribution of the proton and neutron densities inside the nuclei obtained
from experimental data. This indicates that $g$ and $f$ have no sense of the
wave functions of quantum physics. But, $h$ provides proper description of
quantum properties of nucleons inside the nucleus. (3) We calculate meson
function $w^{0}$ and potential $V_{w}$ in RMF theory based on the found nucleon
density. (4) $f$ and $g$ are not solutions of Dirac equation with $V_{w}$. If
the meson theory describes quantum properties of nucleus well, then a
difference between $V_{w}$ and $V_{RMF}$ should be as small as possible. We
introduce new quantum corrections characterizing difference between these
potentials. We find that (a) The function $w^{0}$ should be reinforced
strongly, (b) The corrections are necessary to describe the quantum properties
of the nuclei.
