报告题目：From Classical to Quantum Mechanics: A Mathematical Approach

报 告 人：Jiashun Liu(刘家舜, Master Student @ DUT - Dalian University of Technology)

报告时间：2026年5月14日（星期四）9:00—9:45

报告地点：6776永利集团114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

摘要: In classical mechanics, observables such as position, momentum, energy, and angular momentum appear to be measurable independently and simultaneously. The state of a particle is described by a point $(q,p)\in\mathbb{R}^3\times\mathbb{R}^3$ in phase space, evolving according to Hamilton's equations.

In quantum mechanics, this picture changes. In this talk, I will first introduce the basic concepts and axioms of quantum mechanics. Then, starting from the Schrödinger equation and the momentum operator in the position representation, I will derive them formally, as an analogy with classical mechanics. Using properties of the Fourier transform, I will also show that the momentum operator becomes a multiplication operator in momentum representation, which is an example of the spectral theorem.