Exact WKB Analysis and TBA Equations for the Stark Effect (2307.03504v3)
Abstract: We apply the exact WKB analysis to a couple of one-dimensional Schroedinger-type equations reduced from the Stark effect of hydrogen in a uniform electric field. By introducing Langer's modification and incorporating the Stokes graphs, we prove the exactness of the Bohr-Sommerfeld quantization conditions for the Borel-resummed quantum WKB periods in the specific parameter regions of the electric field intensity and magnetic quantum number. It is also found these quantization conditions get modified with an additional suppressed contribution when the parameters vary beyond the specific regions. We also present Thermodynamic Bethe Ansatz (TBA) equations governing the quantum periods in the absence of Langer's modification and discuss its wall-crossing and analytic continuation. Numerical calculations are conducted to compare the complex resonant frequencies from our quantization conditions against ones from the Riccati-Pade method, the TBA equations are also confirmed by comparing its expansions with all-order quantum periods.
- American Mathematical Soc., 2005.
- K. Imaizumi, Applications of Exact WKB analysis to Spectral problems and 𝒩=2𝒩2\mathcal{N}=2caligraphic_N = 2 gauge theories. Ph.D. thesis, Tokyo Institute of Technology, 2023.
- Academic press, 2014.
- F. M. Fernández and J. Garcia, Comment on “Stark effect in neutral hydrogen by direct integration of the Hamiltonian in parabolic coordinates”, Phys. Rev. A 91 (2015) 066501.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.