  The time-like naked singularities of the electrically and magnetically
charged black hole solutions obtained in a model of nonlinear electrodynamics
proposed by Kruglov is investigated within the framework of quantum mechanics.
In view of quantum mechanics, the space-time is quantum regular provided that
the time evolution of the test quantum wave packet uniquely propagates on an
underlying background. Rigorous calculations have shown that when the
singularity is probed with specific quantum wave/particle modes, the quantum
wave operator turns out to be essentially self-adjoint. Thus, the time
evolution of the quantum wave/particle is determined uniquely. In the case of
electrically charged black hole background, the unique evolution is restricted
to s-wave only. For the two different magnetically charged black hole
backgrounds, the time evolution is restricted to different modes for each case.
