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WKB to all orders and accuracy of the semiclassical quantization

Marko Robnik·Luca Salasnich
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Abstract

We perform a systematic WKB expansion to all orders for a one--dimensional system with potential $V(x)=U_0/\cos^2{(αx)}$. 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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Marko Robnik, Luca Salasnich. 1996-08-08. WKB to all orders and accuracy of the semiclassical quantization. https://arxiv.org/abs/chao-dyn/9608007

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