Work

TBA equations for the Schrödinger equation with a regular singularity

Year: 2020

Type: article

Abstract: We derive the thermodynamic Bethe ansatz (TBA) equations for the Schrödinger equation with an arbitrary polynomial potential and a regular singular (simple and double pole) term. The TBA equations provide a non-trivial generalization of the ODE/IM correspondence and also give a solution for the Riemann–Hilbert problem in the exact WKB method. We study the TBA equations in detail for the linear and the harmonic oscillator potentials together with inverse and centrifugal terms. As an application, we also compute numerically the Voros spectrum for these potentials using the Bohr–Sommerfeld quantization condition.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ab96ee

Authors: Katsushi Ito, Hongfei Shu

Institutions: Tokyo Institute of Technology, Stockholm University, KTH Royal Institute of Technology

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze