WANG Shuchao;ZHANG An;ZHANG Shaohe;SHI Xiaolan;

• 1:Beijing National Day School

Abstract：

The transition courses between high school and university not only bridge the gap between high school and university physics content, but also need to have a certain depth in some aspects. Some knowledge points are already difficult for college students, and for middle school students with weaker mathematical and physical foundations and less knowledge reserve, the difficulty is even greater. At this time, teachers need to design examples skillfully and help students overcome difficulties through appropriate guidance, explanation, comparison, and induction. This paper takes the evolution of wave functions in time-dependent Hamiltonian systems as an example. By skillfully designing examples and comparing incorrect and correct solutions, students can deeply understand the necessity of introducing the time-ordering operator and naturally introduce the time-ordering operator. Finally, a summary of the time-evolution operator is provided.

Key Words： transition from high school to university;time-dependent Hamiltonian;Schr??dinger equation;time-ordering operator

Abstract:

Keywords:

Foundation: 北京市教育科学“十四五”规划2024年度重点课题“基于物理学科大中衔接课程的优秀中学生培养的行动研究”（课题批准号：CADA24053）

Authors: WANG Shuchao;ZHANG An;ZHANG Shaohe;SHI Xiaolan;

References：

• [1]尹亚玲,谭毅,陈佳妮,等.“大中衔接”视角下的高中物理科普课程设计——以“激光应用”教学为例[J].物理教学,2025,47(1):32-35,31.YIN Y L, TAN Y, CHEN J N, et al. Design of high school physics outreach courses from the perspective of secondarytertiary curriculum articulation:A case study of“Laser Applications” in Teaching[J]. Physics Teaching, 2025, 47(1):32-35, 31.
• [2]张燕怡,刘娜.基于“大中衔接”的超导物理科普教学设计[J].物理教学,2017,39(12):4-7,45.ZHANG Y Y, LIU N. Design of outreach teaching in superconductivity based on the perspective of secondary-tertiary curriculum articulation[J]. Physics Teaching, 2017,39(12):4-7, 45.
• [3]王向斌,沈艺鑫,于云龙,等.量子力学基础教程[M].北京:清华大学出版社,2023:11.WANG X B, SHEN Y X, YU Y L, et al. Fundamentals of quntum mechanics[M]. Beijing:Tsinghua University Press, 2023:11.(in Chinese)