“Tracing to the Source” and “Returning” Promoting Deep Understanding of Core Concepts in Structural Chemistry:Cognitive Logic Reconstruction of Time-Independent Schrödinger Equation
LI Hai-Bei1**, SHA Sha1, WANG Xin-Yan1, SONG Cui1, ZHOU Mei-Juan2, QIAO Li-Na1, QI Ming-Ying1
Abstract The time-independent Schrödinger equation is a core and challenging topic in Structural Chemistry.Students often struggle with understanding the essence of mechanical quantity operators and lack a clear physical interpretation of the eigenvalue equation.This paper proposes a novel instructional design centered on the cognitive progression of “from the known to the unknown,from physics to mathematics,and back to physics”. Through graphical teaching,this design guides students to first “trace to the source” in the field of linear algebra,intuitively grasping the concepts of operators,eigenvalues,and eigenvectors.It then leads students to “return”,establishing relationship between abstract mathematical tools and physical mechanical quantities,eigenstates,and eigenvalues,thereby deeply revealing the physical significance of the time-independent Schrödinger equation as an energy eigenvalue equation.Finally,the design applies these concepts to chemistry,enabling students to independently write down the time-independent Schrödinger equation for atomic systems.Our findings indicate that this cognitive logic framework significantly enhances student learning outcomes,fostering a deep understanding of core quantum mechanics concepts and enabling autonomous construction of knowledge frameworks.
LI Hai-Bei, SHA Sha, WANG Xin-Yan, SONG Cui, ZHOU Mei-Juan, QIAO Li-Na, QI Ming-Ying. “Tracing to the Source” and “Returning” Promoting Deep Understanding of Core Concepts in Structural Chemistry:Cognitive Logic Reconstruction of Time-Independent Schrödinger Equation[J]. Chinese Journal of Chemical Education, 2026, 47(14): 22-27.
