一维无限深势阱定态波函数动量展开讨论

Discussion on the Momentum of One Dimensional Infinite Potential Well Stationary Wave Function

一维无限深势阱定态的动量概率分布存在两种“互相矛盾”的结论.为帮助学生理解两种结论的异同,锻炼严谨的科学作风和解决复杂问题的能力,笔者在量子力学理论教学中指导学生利用Python等现代科学计算工具,将一维无限深势阱定态波函数动量展开的讨论进行数值求解与可视化,绘制了不同观点以及不同情形下粒子的动量概率分布图.以此为基础讨论了不同计算结果的物理含义,揭示了两种结论的内在联系.此创新性的举措不仅有效加深了学生对于该重要问题的理解,还促进了学生专业知识、科学能力和综合素质的全面培养.

There exist two different approaches about the probability distribution of momentum for a particle in a one dimensional infinite well.To illustrate the differences and connections between these two approaches,modern teaching techniques including Python was introduced to the course Quantum Mechanics.Students were guided to visualize solutions for different approaches under various conditions.Using this method,the meaning of the results was discussed,and the underlying connections were clarified to the students.This initiative not only effectively deepens students'understanding of this important issue,but also promotes the comprehensive cultivation of students'professional knowledge,scientific ability and comprehensive quality.