角动量算符与轨道波函数  

THE ORBITAL ANGULAR MOMENTUM OPERATOR AND ORBITAL WAVE FUNCTION

作　　者：王建伟 齐海啸 

机构地区：[1]喀什大学物理与电气工程学院,新疆喀什844008

出　　处：《物理与工程》2015年第6期31-36,40,共7页Physics and Engineering

摘　　要：稀土元素、锕系元素的价电子都处于f态,研究价电子轨道角动量问题是量子力学中重要的课题.在量子力学教科书中只给出了氢原子L_2、L_z算符共同本征矢的递推公式,没有计算出L_x、L_y的本征矢;只给出了氢原子的s、p和d电子L_2、L_z算符共同本征矢,没有给出f电子L_2、L_z算符共同本征矢.本文运用表象理论和氢原子L_2、L_z本征矢的递推公式不仅求出了氢原子f电子L_2、L_z算符的共同本征矢,而且还计算出氢原子f电子L_x、L_y的本征矢,并讨论了它们的有关性质.这对于全面了解氢原子电子轨道运动的细节是有好处的,完善了教科书中的不足.Valence electrons of both rare earth elements and actinides are in the f state. So study of orbital angular momentum problem of valence electron is an important topic in quantum mechanics. In quantum mechanics textbooks, only the recursive formula of common eig- envectors for L^2 andL^z operators of hydrogen atom is given, without the calculation of eigenvectors for L^x and L^y The given common eigenvectors for L^2 and L^z operators only corresponds to the electrons on s, p and d orbitals of the hydrogen atom, not including the f orbital. In this paper, using representation theory and the recursive formula of common eigenvectors for L^2 and L^z operators, we not only calculated the common eigenvectors for L^2 and L^z operators of f electrons in hydrogen atom, but also gave the eigenvectors for L^x and L^y operators of f electrons. Relevant properties of these eigenvectors are discussed. This is good for a comprehensive understanding of the details of the atomic orbital motion of the hydrogen atom, and an improvement of the deficiencies in the textbook.

关 键 词：轨道角动量 本征矢 本征值 表象理论 

分 类 号：O413.1-4[理学—理论物理] G642[理学—物理]