物理与工程2025，Vol.35Issue(3)：50-56,7.
外加电磁场下无质量狄拉克方程的严格解
THE EXACT SOLUTION OF THE MASSLESS DIRAC EQUATION IN THE PRESENCE OF AN EXTERNAL ELECTROMAGNETIC FIELD
摘要
Abstract
Graphene,as a cutting-edge research field,holds significant demonstrative value for quantum mechanics education through the solution of its eigenvalue problems.In this paper,taking graphene as an example,we propose a relatively concise method for the exact solution of the eigenvalue problem of the massless Dirac equation in the presence of an external electro-magnetic field.This method is based on the principles of relativistic quantum theory by Lan-dau and Lifshitz,and with the help of the well-known eigenvalue solution of one-dimensional harmonic oscillator model the eigenenergy and the eigenstate are obtained by cleverly resolving the Dirac equation.The results show that in the graphene physical system under an external electromagnetic field,the electric field causes a contraction in the spacing between adjacent Landau levels,eventually leading to a sudden collapse of the entire Landau spectrum at the critical value of β=1.This interesting physical phenomenon does not occur in the non-relativ-istic standard two-dimensional electron gas system.The solution of the eigenvalue problem of graphene can demonstrate the application of quantum mechanics in condensed matter physics and materials science.Students can learn how to use quantum mechanics theory to explain and predict the electronic properties of graphene,such as its band structure and conductivity.This helps to enhance students' understanding of the connection between quantum mechanics theo-ry and its practical applications,and improves their comprehension of quantum effects in con-densed matter physics and materials science.关键词
石墨烯/电磁场/狄拉克方程/本征值Key words
graphene/electromagnetic field/Dirac equation/eigenvalue引用本文复制引用
马宁..外加电磁场下无质量狄拉克方程的严格解[J].物理与工程,2025,35(3):50-56,7.基金项目
国家自然科学基金(11305113) （11305113）
山西省自然科学基金面上项目(202303021221047) （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). （2019JG059）
