Investigation on onedimensional infinite square well: a threedimensional framework based on a classical collision model

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  • 1. College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen, Guangdong 518060, China;
    2. College of Electronics and Information Engineering,Shenzhen University, Shenzhen, Guangdong 518060, China

Received date: 2025-06-27

  Accepted date: 2025-10-21

  Online published: 2026-08-28

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.

Cite this article

SUN Lei1, 2, WU Kedi1, 2 . Investigation on onedimensional infinite square well: a threedimensional framework based on a classical collision model[J]. College Physics, 2026 , 45(6) : 35 . DOI: 10.16854/j.cnki.1000-0712.250336

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