物理与工程2025，Vol.35Issue(2)：78-83,6.
晶体场劈裂在量子力学简并态微扰教学中的应用
APPLICATION OF CRYSTAL-FIELD SPLITTING IN TEACHING THE PERTURBATION THEORY OF DEGENERATE STATES IN QUANTUM MECHANICS COURSE
摘要
Abstract
To address the scarcity of examples for degenerate perturbation in quantum me-chanics,this paper proposes crystal-field splitting as a new example for teaching degenerate perturbations.Starting from the construction of the octahedral crystal field,this part of the content first calculates the perturbation potential based on Coulomb interaction.Then,it se-lects the single d-electron wave function to calculate the perturbation matrix elements,there-by constructing the secular matrix.The calculation process involves integrating the angular and radial parts separately,which relates to the knowledge of angular momentum.Finally,through diagonalization,the splitting of energy levels after perturbation and the linear combi-nation of zero-order wave functions are obtained.Furthermore,based on the fundamental properties of degenerate states,their real function forms are derived.This example will help students understand the degenerate perturbation at a deeper level.关键词
量子力学/简并态微扰/晶体场/能级劈裂Key words
quantum mechanics/degenerate perturbation/crystal-field/energy level splitting引用本文复制引用
宋振,杨善武,滕蛟,高霞,张铮,刘泉林..晶体场劈裂在量子力学简并态微扰教学中的应用[J].物理与工程,2025,35(2):78-83,6.基金项目
国家自然科学基金(12274023) （12274023）
北京科技大学本科教育教学改革面上项目(JG2021M07). （JG2021M07）
