2020/06/30 by B. M. Tripathi, B. Tripathi · 3 citations
Mathematics · Physics and Astronomy · #Asymptotic expansion #Bohr model #Brillouin zone #Cold Atom Physics and Bose-Einstein Condensates #Mathematical analysis #Mathematics #Physics #Quantization (signal processing) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Series (stratigraphy) #Statistics #Sublinear function #WKB approximation #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevd.105.036010
published in Physical review. D/Physical review. D. 105(3) (American Physical Society) · Published in PRD. Comments are welcome. Note the simplicity of the formula. https://link.aps.org/doi/10.1103/PhysRevD.105.036010
openalex created_date 2021/10/25 · arxiv created 2022/02/22 · openalex publication_date 2022/02/22 · arxiv updated 2022/02/23 · openalex updated_date 2026/08/05
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 problems. The formula is elegantly interpreted as the action evaluated using the product of spatially varying wave number and a coefficient related to the wave transmissivity; unit transmissivity yields the Bohr-Sommerfeld quantization.