SETTING UP COMPARATIVE EXAMPLES TO ADDRESS DIFFICULTIES IN THE TRANSITION FROM HIGH SCHOOL TO UNIVERSITY COURSES: INSIGHTS FROM TWO "SOLUTIONS" TO A SAMPLE PROBLEM ON WAVE FUNCTION EVOLUTION IN TIME-DEPENDENT HAMILTONIAN SYSTEMS

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.