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Paper detail

Resummed Wentzel-Kramers-Brillouin Series: Quantization and Physical Interpretation

The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and at best, asymptotic, thus impeding predictions beyond the first few leading-order effects. Here, we report a closed-form formula that exactly resums the perturbative WKB series to all-orders for two turning point problem. The formula is elegantly interpreted as the action evaluated using the product of spatially-varying wavenumber and a coefficient related to the wave transmissivity; unit transmissivity yields the Bohr-Sommerfeld quantization.

preprint2022arXivOpen access
B. Tripathi
math-phmath.MPquant-ph
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B. Tripathi

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