Colloquium / Seminars

Topic：A brief introduction to semiclassical analysis for Schrödinger equations
Speaker：Prof. Chiun-Chang Lee
　　　　(National Tsing Hua University)
Date time：May 28, 2024 14:00 15:00
Venue：SA223
Abstract：
Abstract. Nonlinear Schrödinger equations are a widely studied topic due to their various applications in nonlinear optics and Bose–Einstein condensates. The semiclassical analysis serves as a link between quantum mechanics and classical mechanics, providing insight into how classical physics emerges from quantum mechanical principles, with Planck's constant playing a crucial role.

In this talk, I will first apply Madelung's transform to the Schrödinger equation and formally derive the hydrodynamic equations. Then, I will introduce a mathematical method for investigating the semiclassical limits of Schrödinger equations. The focus will be on introducing a modulated energy functional to govern mass density and linear momentum, particularly in relation to the compressible Euler equations. Finally, I will introduce my ongoing work about a nonlocal Schrödinger equation, drawing connections to a nonlocal compressible Euler equation.
Download：Talk_1130528.pdf

$返回$ go back