关键词: 一维量子体系, 数值计算, 有限差分

Abstract: A Python-based teaching code has been developed to numerically verify fundamental quantum mechanical concepts, such as orthonormality, eigen spectrum, and uncertainty relations. This tool is applicable for teaching or conducting numerical experiments in structural chemistry courses for students majoring in Chemistry, Materials Science, and related fields. The techniques described can be extended to more complex one-dimensional systems, including harmonic and anharmonic oscillators, the radial wavefunctions of hydrogen-like atoms, and double or multiple potential wells, which are common problems in chemistry. Teaching practices in materials chemistry program at UPC have shown that most students can understand the material and independently implement computational codes, thereby deepening their comprehension of course content.

Key words: One-dimensional quantum system, Numerical calculations, Finite-difference