马宁

• 1:太原理工大学物理与光电工程学院

摘要(Abstract)：

石墨烯作为一个前沿的研究领域，其本征值问题的求解对量子力学教学具有重要的示范意义。本文以石墨烯为例，提出了严格求解外加电磁场下无质量狄拉克方程本征值问题的一种较为简洁的方法，即基于朗道和栗弗席兹的相对性量子理论原理，并借助一维谐振子模型众所周知的本征值解巧妙地解析得到了狄拉克方程的本征能量和本征波函数。结果表明，在外加电磁场的石墨烯物理系统中，电场会使得相邻朗道能级间隔发生收缩，并最终导致整个朗道能谱在β=1的临界值处突然发生塌缩，这一有趣的物理现象在非相对论性的标准二维电子气系统中并未出现。石墨烯本征值问题的求解，可以展示量子力学在凝聚态物理和材料科学中的应用。学生可以学习如何使用量子力学理论来解释和预测石墨烯的电学性质，如能带结构和导电性等。这有助于增强学生对量子力学理论与实际应用之间的联系，提高他们对凝聚态物理和材料科学中量子效应的理解。

关键词(KeyWords)： 石墨烯;电磁场;狄拉克方程;本征值

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11305113);; 山西省自然科学基金面上项目(202303021221047);; 山西省高等学校教学改革创新项目(J20230219;J2019057);; 山西省研究生教育改革研究课题项目(2019JG059)

作者(Author): 马宁

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