  We perform a systematic WKB expansion to all orders for a one-dimensional
system with potential $V(x)=U_0/\cos^2{(\alpha x)}$. We are able to sum the
series to the exact energy spectrum. Then we show that at any finite order the
error of the WKB approximation measured in the natural units of the mean energy
level spacing does not go to zero when the quantum number goes to infinity.
Therefore we make the general conclusion that the semiclassical approximations
fail to predict the individual energy levels within a vanishing fraction of the
mean energy level spacing.
