  A quantum mechanical model of two interacting electrons in graphene is
considered. We concentrate on the case of zero total momentum of the pair. We
show that the dynamics of the system is very unusual. Both stationary and
time-dependent problems are considered. It is shown that the complete set of
the wave functions with definite energy includes the new functions, previously
overlooked. The time evolution of the wave packet, corresponding to the
scattering problem setup, leads to the appearance of the localized state at
large time. The asymptotics of this state is found analytically. We obtain the
lower bound of the life time of this state, which is connected with the
breakdown of the continuous model on the lattice scale. The estimate of this
bound gives one a hope to observe the localized states in the experiment.
