均匀电磁场中一维线性谐振子的能级研究  

Study on the Level of One-dimensional Linear Harmonic Oscillator in the Uniform Electromagnetic Field

作　　者：赵森 崔久波 张海丰[1] 齐若杉 肖逍 庞福荣 ZHAO Seng;CUI Jiu-bo;ZHANG Hai-feng;QI Ruo-shan;XIAO Xiao;PANG Fu-rong(College of Science, Jiamusi University, Jiamusi Heilongjiang 154007,China)

机构地区：[1]佳木斯大学理学院

出　　处：《佳木斯大学学报（自然科学版）》2019年第5期849-852,共4页Journal of Jiamusi University：Natural Science Edition

基　　金：国家自然科学基金项目(51141009);佳木斯大学科学技术研究面上项目(Ljz2012-14);佳木斯大学大学生创新创业项目(2019xj25);黑龙江省基本科研业务费基础研究项目(2018-kYYWF-0956)

摘　　要：通过严格求解薛定谔方程给出了均匀电场、常磁场中的一维线性谐振子的能级分布进行了讨论,同时给出了考虑自旋的情况下的常磁场中的谐振子能级。结果表明均匀电场中的一维线性谐振子能量算符的本征波函数是标准的以y为变量的函数,而本征函数作为x的函数是不同的;常磁场中一维线性谐振子的能级和波函数是可以严格求解的;考虑自旋的常磁场中的一维线性谐振子的薛定谔方程的解为朗道能级。By strictly solving the Schrodinger equation, the level distributions of a one-dimensional linear harmonic oscillator in a uniform electric field and a constant magnetic field are discussed. The results show that the eigen wave function of the energy operator of one-dimensional linear harmonic oscillator in uniform electric field is a standard function with y as a variable, while the eigen function is different as a function of x. The energy level and wave function of the one-dimensional linear harmonic oscillator in a constant magnetic field can be solved strictly. Finally, the solution of the Schrodinger equation for the linear harmonic oscillator in a spin constant magnetic field is the landau level when the spin is considered.

关 键 词：均匀电场 常磁场 线性谐振子 能级分布 

分 类 号：O431[机械工程—光学工程]