  When using the quantum mechanical second-order equation with the effective
potential of the Kerr-Newman (KN) field for fermions, results were obtained
that qualitatively differ from results obtained when using the Dirac equation.
In presence of two event horizons, existence of degenerate stationary bound
states was proved for charged and uncharged fermions with square integrable
wave functions vanishing on event horizons. The fermions in such states are
localized near the event horizons with the maxima of probability densities away
from the event horizons by fractions of the Compton wave length of fermions
versus the values of coupling constants, the values of angular and orbital
momenta $j,l$ and the value of the azimuthal quantum number $m_{\varphi}$. In
the case of extreme KN fields, absence of stationary bound states of fermions
was shown for any values of coupling constants. Existence of discrete energy
spectra was shown for charged and uncharged fermions in the field of naked KN
singularity at definite values of physical parameters. The KN naked singularity
poses no threat to cosmic censorship because of the regular behavior of the
effective potentials of the KN field in quantum mechanics with the second-order
equation.
