From Single Particles to Many-body Systems: the Practice of Exact Diagonalization in Computational Physics Teaching
Year: 2025
Type: article
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.
Source: Wuli yu gongcheng.
Authors: Hanqing WU, Daoxin YAO
Institution: Sun Yat-sen University
Language: English
Subfield: Education
Field: Social Sciences
Domain: Social Sciences
SDG: Quality education
Open Access status: bronze
OpenAlex ID: W7127938361
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