关键词: 一维无穷深势阱, 经典碰撞模型, 量子思维范式

Abstract: This paper addresses the prevalent issue in undergraduate quantum mechanics instruction of the onedimensional infinite square well, where mathematical derivation is prioritized over physical imagery, proposing a restructured teaching approach through a threedimensional “physical imagerymathematical formalismclassical limit” framework by introducing a classical collision model as a cognitive bridge—where the physical imagery dimension visually demonstrates kineticpotential energy conservation to clarify boundary origins and correct “classical deep well” misconceptions; the mathematical formalism dimension employs dimensional analysis and probability density analogies to imbue energy parameters and boundary conditions with physical meaning; and the classical limit dimension contrasts average probability density and zeropoint energy with classical models to reveal quantum systems’ essential characteristics, with practice confirming this strategy effectively helps students overcome cognitive biases, grasp core concepts like wave function statistical interpretation and energy quantization, and establish a quantum thinking paradigm.

Key words: onedimensional infinite square well, classical collision model, paradigm of quantum thinking