Resummed Wentzel-Kramers-Brillouin Series: Quantization and Physical Interpretation
arXiv:2006.01434 · doi:10.1103/PhysRevD.105.036010
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.
Published in PRD. Comments are welcome. Note the simplicity of the formula. https://link.aps.org/doi/10.1103/PhysRevD.105.036010