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

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

URL: http://arxiv.org/abs/2006.01434v3
Date: Tue, 22 Feb 2022 16:29:34 GMT
Title: Resummed Wentzel-Kramers-Brillouin Series: Quantization and Physical Interpretation
Authors: B. Tripathi
Abstract summary: The Wentzel-Kramers-Brillouin (WKB) perturbative series is typically divergent and at best, 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.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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