  In the present paper we examine the accuracy of the quasiclassical approach
on the example of small-angle electron elastic scattering. Using the
quasiclassical approach, we derive the differential cross section and the
Sherman function for arbitrary localized potential at high energy. These
results are exact in the atomic charge number and correspond to the leading and
the next-to-leading high-energy small-angle asymptotics for the scattering
amplitude. Using the small-angle expansion of the exact amplitude of electron
elastic scattering in the Coulomb field, we derive the cross section and the
Sherman function with a relative accuracy $\theta^2$ and $\theta^1$,
respectively ($\theta$ is the scattering angle). We show that the correction of
relative order $\theta^2$ to the cross section, as well as that of relative
order $\theta^1$ to the Sherman function, originates not only from the
contribution of large angular momenta $l\gg 1$, but also from that of $l\sim
1$. This means that, in general, it is not possible to go beyond the accuracy
of the next-to-leading quasiclassical approximation without taking into account
the non-quasiclassical terms.
