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Citation: Hao Ren, Wen Zhao, Fangna Dai, Wenyue Guo. Finite Difference Solution of One-Dimensional Quantum Systems: (1) Fundamental Concepts and Infinite Square Well[J]. University Chemistry, ;2025, 40(3): 124-131. doi: 10.12461/PKU.DXHX202405145 shu

Finite Difference Solution of One-Dimensional Quantum Systems: (1) Fundamental Concepts and Infinite Square Well

Shandong Key Laboratory of Intelligent Energy Materials, School of Materials Science and Engineering, China University of Petroleum (East China), Qingdao 266580, Shandong Province, China

Corresponding author: Hao Ren, renh@upc.edu.cn
Received Date: 22 May 2024
Revised Date: 15 August 2024

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.
- One-dimensional quantum system,
- Numerical calculations,
- Finite-difference
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