多势阱中电子的束缚态与能带形成研究

doi:10.3969/j.issn.1007-5461.2021.03.007

量子电子学报 ›› 2021, Vol. 38 ›› Issue (3): 316-326.doi: 10.3969/j.issn.1007-5461.2021.03.007

多势阱中电子的束缚态与能带形成研究

江俊勤∗, 涂菁

广东第二师范学院物理与信息工程系, 广东广州510303

收稿日期:2020-06-29 修回日期:2020-09-08 出版日期:2021-05-28 发布日期:2021-05-28
通讯作者: 502687985@qq.com
作者简介:江俊勤( 1962 - ), 广东揭阳人, 教授, 主要从事格点规范场论和量子物理方面的研究。E-mail: 502687985@qq.com

Study on electronic bound states in multiple-well potential and formation of energy band

JIANG Junqin∗, TU Jing

Department of Physics and Information Engineering, Guangdong University of Education, Guangzhou 510303, China

Received:2020-06-29 Revised:2020-09-08 Published:2021-05-28 Online:2021-05-28

摘要/Abstract

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0.5 nm 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。

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

Abstract: 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.

Key words: quantum physics, energy level and wave function, linear equations, quantum well, numerical calculation, energy band

中图分类号:

O413.1

江俊勤∗, 涂菁. 多势阱中电子的束缚态与能带形成研究[J]. 量子电子学报, 2021, 38(3): 316-326.

JIANG Junqin∗, TU Jing. Study on electronic bound states in multiple-well potential and formation of energy band[J]. Chinese Journal of Quantum Electronics, 2021, 38(3): 316-326.

参考文献 13

[1]	Zhang L, Xie H J, Chen C Y, et al. Structures of the energy levels of the bound states in a quantum dot quantum well [J].
	Chinese Journal of Quantum Electronics, 2003, 20(3): 338-344.
	张立, 谢洪鲸, 陈传誉, 等. 量子点量子阱中束缚态的能级结构[J]. 量子电子学报, 2003, 20(3): 338-344.
[2]	Xin P, Sun C W, Qin F W, et al. Room-temperature photoluminescence of ZnO /MgO multiple quantum wells deposited by
	reactive magnetron sputtering [J]. Acta Physica Sinica, 2007, 56(2): 1082-1087.
	辛萍, 孙成伟, 秦福文, 等. 反应磁控溅射ZnO/MgO 多量子阱的光致荧光光谱分析[J]. 物理学报, 2007, 56(2): 1082-1087.
[3]	Duan Y T, Xu Y G, Lin Q L, et al. Characteristics of energy level splitting in double potential well [J]. Journal of Shaanxi
	Normal University (Natural Science Edition), 2013, 41(5): 42-45.
	段艳涛, 徐永刚, 林钱兰, 等. 双势阱中能级分裂的物理机理探析[J]. 陕西师范大学学报(自然科学版), 2013, 41(5): 42-45.
[4]	Chen L,Wang H L, Chen S, et al. Effect of external field on exciton binding energy in InPBi quantum well [J]. Chinese Journal
	of Quantum Electronics, 2017, 34(1): 117-122.
	陈丽, 王海龙, 陈莎, 等. 外场对InPBi 量子阱中激子结合能的影响[J]. 量子电子学报, 2017, 34(1): 117-122.
[5]	曾谨言. 量子力学教程[M]. 北京: 科学出版社, 2003: 34-36.
[6]	周世勋. 量子力学教程[M]. 北京: 高等教育出版社, 2009: 45.
[7]	苏如铿. 量子力学[M]. 上海: 复旦大学出版社, 1997: 37-40.
[8]	朱栋培. 量子力学基础[M]. 合肥: 中国科学技术大学出版社, 2012: 41-46.
[9]	董键. Mathematica 与大学物理计算[M]. 北京: 清华大学出版社, 2010: 309-318.
[10]	Jiang J Q, Shen H J. Numerical study of electronic states in finite multiple potential wells [J]. College Physics, 2016, 35(11):
13	-17.
	江俊勤, 沈华嘉. 有限深多势阱中电子能态的数值研究[J]. 大学物理, 2016, 35(11): 13-17.

[1]	张超, 管致锦, 冯世光, 牛义仁, 朱明强. 一种二维架构下的量子电路布局与优化方法[J]. 量子电子学报, 2023, 40(4): 570-581.
[2]	王长, ∗ , 宋高辉, , 谭智勇, , 曹俊诚, ∗. 基于半导体光子学器件的太赫兹成像技术研究进展 (封面文章}[J]. 量子电子学报, 2023, 40(2): 181-192.
[3]	红兰∗, 戈君, 双山, 刘达权. 非对称量子阱中磁极化子的性质[J]. 量子电子学报, 2022, 39(5): 728-735.
[4]	刘星灿哈斯花. 随机势场对氢原子能量本征问题的影响[J]. 量子电子学报, 2021, 38(4): 436-443.
[5]	张建芳, 肖景林∗. 非对称半指数量子阱中强耦合极化子振动频率[J]. 量子电子学报, 2020, 37(6): 699-703.
[6]	黄欣1，方卉1，霍艺芝1，巩龙延1,2*. 电子在长程跳跃随机势模型中的波粒二象性[J]. 量子电子学报, 2019, 36(2): 156-160.
[7]	张海瑞1，丽英1，高宽云2. 三角量子阱中弱耦合极化子声子平均数研究[J]. 量子电子学报, 2018, 35(6): 743-746.
[8]	张金凤1，李腾2 . 导带弯曲对有限深量子阱中激子态影响的研究[J]. 量子电子学报, 2018, 35(6): 747-751.
[9]	单淑萍. 三角量子阱中极化子的Rashba效应[J]. J4, 2018, 35(5): 625-630.
[10]	吴德伟李响杨春燕苗强. 基于超导约瑟夫森结的双路径量子纠缠微波信号研究进展[J]. J4, 2017, 34(1): 1-8.
[11]	陈莎王海龙陈丽李正龚谦. Cd1-xMnxTe/CdTe量子阱中电子-LO声子散射率[J]. J4, 2017, 34(1): 94-98.
[12]	陈丽王海龙陈莎李正李士玲龚谦. 外场对InPBi量子阱中激子结合能的影响[J]. J4, 2017, 34(1): 117-122.
[13]	徐中辉姜芸李艳玲黄劲松陈宇光. 具有Stubs结构量子波导中电子的自旋传输特性[J]. J4, 2016, 33(5): 628-634.
[14]	高宽云邢海峰. 抛物量子阱中强耦合极化子的声子平均数[J]. J4, 2016, 33(5): 635-640.
[15]	文林芳方建兴. 塞曼能级电磁诱导透明暗态的演化[J]. J4, 2015, 32(6): 706-712.

多势阱中电子的束缚态与能带形成研究

Study on electronic bound states in multiple-well potential and formation of energy band

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献 13

相关文章 15

编辑推荐

Metrics

本文评价