WKB to all orders and accuracy of the semiclassical quantization
  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 any finite order WKB approximation fails to predict the individual energy levels within a vanishing fraction of the mean energy level spacing. 
Marko Robnik and Luca Salasnich