@article{WU2025, 
author = {Hanqing WU and Daoxin YAO},
title = {FROM SINGLE PARTICLES TO MANY-BODY SYSTEMS: THE PRACTICE OF EXACT DIAGONALIZATION IN COMPUTATIONAL PHYSICS TEACHING},
year = {2025},
journal = {Physics and Engineering},
volume = {35},
number = {6},
pages = {5-12},
keywords = {quantum mechanics, exact diagonalization, stationary Schrödinger equation, many-particle system, many-body basis},
url = {https://www.sciopen.com/article/10.26599/PHYS.2025.9320601},
doi = {10.26599/PHYS.2025.9320601},
abstract = {Exact diagonalization serves as the most intuitive numerical approach for solving quantum problems and is widely applied in both few-body and many-body systems, making it a core component of computational physics curricula. Guided by a scaffolded teaching philosophy that progresses from fundamental to advanced concepts, this paper systematically outlines the instruction of exact diagonalization in undergraduate computational physics courses—beginning with single-particle systems and gradually advancing to quantum many-body systems. Through a series of carefully designed pedagogical examples, students not only master key procedural steps such as basis selection, symmetry utilization, matrix construction, and diagonalization, but also develop a deeper comprehension of the method's strengths and limitations. This instructional framework effectively bridges the formalism of quantum mechanics with cutting-edge many-body numerical techniques, laying a solid groundwork for students' future exploration of advanced many-body computational methods such as the density matrix renormalization group and tensor networks.}
}