WKB to all orders and accuracy of the semiclassical quantization
classification
chao-dyn
nlin.CD
keywords
energyordersableaccuracyalphaapproximationexactexpansion
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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.
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