WKB to all orders and accuracy of the semiclassical quantization

Details WKB to all orders and accuracy of the semiclassical quantization WKB to all orders and accuracy of the semiclassical quantization

1996-08-08

arxiv.org/abs/chao-dyn/9608007v1

Nonlinear Sciences

Chaotic Dynamics

11 pages, latex, no figures, Preprint CAMTP/96-5, July 1996, submitted to J. Phys. A: Math. Gen

Scientific paper

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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