WU Hanqing;YAO Daoxin;

• 1:School of Physics
• 2: Sun Yat-sen University

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.

Key Words： exact diagonalization;quantum mechanics;stationary Schr??dinger equation;many-particle system;many-body basis

Abstract:

Keywords:

Foundation: 国家自然科学基金面上项目(12474248);; 中山大学2024年度校级教学质量工程项目(教务[2023]207号)

Authors: WU Hanqing;YAO Daoxin;

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