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TBA system and Schrödinger equation

14/11/2019 dalle 14:00 alle 16:00

Dove Aula Teorici, piano 2, via Irnerio 46, Bologna

Contatto di riferimento

Partecipanti Dr. Hongfei Shu (Nordita - Sweden)

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Abstract: 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].