Title：Solvingthe Schrödinger equationby using integrability

Speaker：束红非(Hongfei Shu)

Time：August 16,2019,15:00PM

Venue：371 Room, Physics Building

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-dimensionalquantum integrable models (IM). In this talk, we focus on the Schrödinger equation of one-dimensional Quantum Mechanics, which is atypical example of the secondorder 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 and angular momentum. 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 also show that our TBA equations, combined with exact quantization conditions, provide a powerful method to solve spectral problems in Quantum Mechanics. We illustrate our general analysis with a detailed study of cubic oscillators. This talk is based on the work with Katsushi Ito and Marcos Marino [arXiv: 1811.04812] and the work in progress.

Brief Bio:

Dr. Hongfei Shu obtained his B.S. at Tokyo Institute of Technology in Japan in 2014, MS in Tokyo Institute of Technology (Prof. Katsushi Ito’s group, Japan) in 2016, and completed his Ph.D. in Tokyo Institute of Technology (Prof. Katsushi Ito’s group, Japan) in 2019. He will move to Nordita Sweden in this fall as postdoc. He received JSPS Research Fellowship for Young Scientists from 2017 to 2019. Currently, he is a special PD researcher in Tokyo Institute of Technology. His research interest includes Integrability, N=2 Gauge theory and AdS/CFT correspondence.