摘要
用经典解法研究了处于N个量子阱中电子的能级和量子态。从定态薛定谔方程出发,由波函数标准条件导出波函数中待定系数满足的(4N-2)元线性方程组。由线性方程组系数行列式等于0的超越方程计算出电子的能级,通过计算线性方程组的基础解系求得束缚定态波函数。在N=2~5、势阱宽度为1 nm、势阱间距为0.5nm的情况下,利用Mathematica软件求得电子能级和波函数的高精度数值解,并直观地展示了电子能级分裂成能带的机理。所提出方法物理概念清晰、过程简明易懂、不存在人为调节的参数,而且计算精度高、速度快。
The energy levels and quantum states of electron in N symmetric potential well are investigated by using classical method.Based on Schr¨odinger equation and the standard conditions of wave function,the(4N−2)-variables linear equations with undetermined coefficients in the wave function are derived.The transcendental equation is obtained from that the coefficient determinant equals to zero.Then the energy levels of electron are calculated by solving the transcendental equation,and the bound state wave function is obtained by calculating the basic solution set of the linear equations.In the case of N=2∼5,well width of 1 nm and well spacing of 0.5 nm,the energy levels and wave functions are calculated numerically by using Mathematica software and the mechanism of the energy level splitting into energy band is exhibited intuitively.It is shown that the physical concept of the proposed method is clear,the process is simple and easy to understand,and in addition,there are no artificially adjusted parameters,and the calculation accuracy is high and the speed is fast.
作者
江俊勤
涂菁
JIANG Junqin;TU Jing(Department of Physics and Information Engineering,Guangdong University of Education,Guangzhou 510303,China)
出处
《量子电子学报》
CAS
CSCD
北大核心
2021年第3期316-326,共11页
Chinese Journal of Quantum Electronics
关键词
量子物理
能级和波函数
线性方程组
量子阱
数值计算
能带
quantum physics
energy level and wave function
linear equations
quantum well
numerical calculation
energy band
