TBA system and Schrödinger equation

by Dr Hongfei Shu (Nordita - Sweden)

Thursday 14 Nov 2019, 14:00 → 16:00 Europe/Rome

Aula Teorici (DIFA)

The ODE/IM correspondence describes the relation between the spectral analysis of ordinary differential equations (ODE) and the functional relations approach of the two-dimensional quantum integrable models (IM). In this talk, we focus on the Schroedinger equation of one-dimensional Quantum Mechanics, which is a typical example of the second order ODE. We derive a system of Thermodynamic Bethe ansatz (TBA) equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and can be regarded as the solution of a Riemann-Hilbert problem in resurgent Quantum Mechanics formulated by Voros. We show that our TBA equations, combined with exact quantization conditions, provide a powerful method to solve spectral problems in Quantum Mechanics. This talk is based on the work with Katsushi Ito and Marcos Marino [arXiv: 1811.04812, 1910.09406].