  The wave equation describing the interaction of two electrons in graphene at
arbitrary value of the Fermi energy $E_F$ is derived. For the solutions of this
equation, we have found the explicit forms of the density and the current which
obey the continuity equation. We have traced the evolution of the wave packet
during a scattering process. It is shown that the long-leaving localized
quasi-stationary peak may appear at $E_F<0$ . Then this peak decays into a set
of wave packets following each other. At $t\rightarrow\infty$ a total norm of
all outgoing wave packets equals to that of incoming wave packet. At $E_F=0$
the localized state does not appear. For $E_F<0$ there is an infinite set of
the localized solutions with the finite norms.
