演講公告
新聞標題： ( 2024-05-23 )
演講主題：A brief introduction to semiclassical analysis for Schrödinger equations
主講人：李俊璋教授(清華大學)
演講日期：2024年5月28日14:00 –15:00
演講地點：(光復校區) 科學一館223室
摘要內容：
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.相關檔案：Talk_1130528.pdf
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