量子力学中表象变换理论的教学探讨:结合中微子振荡的前沿案例  

Study on the teaching of representation transformation theory in quantum mechanics:combining frontiers of neutrino oscillations

作　　者：涂涛[1] 郭奥林 李传锋[1] 郭光灿[1] TU Tao;GUO Ao-lin;LI Chuan-feng;GUO Guang-can(School of Physics,Key Lab of Quantum Information of Chinses Academy,Universityof Science and Technology of China,Hefei Anhui 230026,China)

机构地区：[1]中国科学技术大学物理学院,中国科学院量子信息重点实验室,安徽合肥230026

出　　处：《大学物理》2022年第8期1-6,70,共7页College Physics

基　　金：安徽省高等学校省级教学研究项目(2020jyxm2286,2020xxsjg01);国家自然科学基金(11474131)资助。

摘　　要：量子力学是物理学专业本科生的基础核心课程,同时其内容又与现代物理学的诸多研究前沿紧密联系在一起.本文针对量子力学中比较抽象的表象变换理论,结合中微子振荡这一研究前沿作为具体的教学案例.在教学中,我们首先引入中微子的味表象和质量表象,然后可以比较直观的建立起两种表象之间的表象变换矩阵,其中的矩阵元具有清晰的物理含义:表示不同中微子质量本征态之间的混合.利用这一表象变换理论,我们可以分析中微子的含时演化行为,并与实验观测到的中微子振荡现象进行比较,发现理论分析能够很好的解释实验现象.在教学中引入这一前沿案例,不但有助于学生们更加直观的理解表象变换理论,而且可以拓展学生们的视野,激发他们进一步深入研究的兴趣和热情.Quantum mechanics is a fundamental core course for undergraduate students in physics major, and its content is closely related to many research frontiers in modern physics. In this paper, we use the abstract formulas of representation transformation theory in quantum mechanics to study a specific case in the context of neutrino oscillations. In the teaching, we first introduce the flavor and mass representations of neutrinos, and then we can build up the representation transformation matrix between the two representations intuitively, where the matrix elements have a clear physical meaning: to represent the mixing angle between different neutrino mass eigenstates. Using this representation transformation theory, we can analyze the time evolution behavior of neutrinos and compare with the experimental neutrino oscillation phenomena. We found that the theoretical analysis can explain the experimental phenomena very well. The introduction of this cutting-edge example in teaching not only helps students to understand the representation transformation theory more intuitively, but also expands their horizons and stimulates their interest and enthusiasm for further research.

关 键 词：量子力学 表象变换理论 中微子振荡 

分 类 号：O413.1[理学—理论物理]