准精确可解（Quasi-Exactly Solvable, QES）系统是一类部分能谱和本征态可通过解析方法求解的量子力学模型．本文以QES周期势为中心，回顾了QES问题的定义、发展历程及其在物理学中的重要性．通过分析Kronig-Penney模型、Lamé势、PT对称周期势和Mathieu势的能带结构，揭示了这些模型在周期性晶格中电子行为的描述中所扮演的关键角色．本文结合李代数、多项式不变子空间及超对称量子力学等理论工具，系统探讨了QES周期势的能带特性及其解析解．结果表明，不同的QES周期势展现了丰富的能带结构，可用于调控晶体材料的带隙．QES系统在解决复杂量子体系中具有重要意义，并为新型材料和非厄米系统的研究提供了理论指导和前瞻性思路．

Quasi-exactly solvable (QES) systems are a class of quantum mechanical models in which part of the energy spectrum and eigenstates can be solved analytically. This paper reviews the definition and development of the QES problem and its importance in physics, centering on the QES periodic potential. By analyzing the energy band structure of the Kronig-Penney model, the Lamé potential, the PT-symmetric periodic potential, and the Mathieu potential, the key role played by these models in the description of the electron behavior in periodic lattices is revealed. In this paper, the energy band properties of the QES periodic potentials and their analytic solutions are systematically explored by combining the theoretical tools of Lie algebra, polynomial invariant subspaces, and supersymmetric quantum mechanics. The results show that different QES periodic potentials exhibit rich energy band structures, which can be used to modulate the bandgap of crystalline materials. The QES system is of great significance in solving complex quantum systems and provides theoretical guidance and prospective ideas for studying novel materials and Non-Hermitian systems.