  We analyze the density of state (DOS) and a non-magnetic impurity effect in
electron-doped cuprates starting from two different scenarios: the
$d_{x^{2}-y^{2}}$-wave superconductivity coexisting with antiferromagnetic spin
density wave (SDW) order versus $d_{x^{2}-y^{2}}$-wave superconductivity with a
higher harmonic. We find that in both cases the local density of state (LDOS)
exhibits two impurity-induced resonance states at low energies. We also find
that for the intermediate value of the SDW gap, the DOS looks similar to that
obtained from the scenario of the $d_{x^{2}-y^{2}}$-wave gap with a higher
harmonic, suggesting the presence of a non-monotonic $d_{x^{2}-y^{2}}$-wave
gap. However, if the SDW gap is sufficiently large the DOS looks more
conventional s-wave like. This obvious difference from the DOS resulted from
the $d_{x^{2}-y^{2}}$-wave gap with a higher harmonic model, could
differentiate the two above scenarios and is needed to be proved in the further
doping dependence of tunneling spectrum measurement.
