基于GUI的三维无限深势阱可视化研究

无限深势阱中粒子的量子力学图像是教师教学和学生学习的一个难点,本文利用Matlab的GUI功能对三维无限深势阱粒子的量子化行为进行可视化研究。通过对控件的选取与设置,分别给出了三维无限深势阱不同量子数下零平面、极值点所在平面的波函数切片分布图,以及垂直x方向任意截面处的波函数立体分布图,实现了三维无限深势阱任意量子数及任意截面处波函数的可视化。利用GUI实现三维无限深势阱粒子量子化行为的可视化,可以很好地实现人机互动,便于形象分析不同条件下的波函数分布情况,有助于教师教学和学生学习。     

一维双势阱问题的理论研究

利用数值计算的方法求解了一维理想双势阱模型的基态及低激发态能级和相应的波函数,将双势阱之间的间距、双势阱的相对深度和双势阱的宽窄与实际的物理问题建立了联系,并分析了它们对一维双势阱的能级和相应波函数的影响,定性地模拟了双原子分子和原子中的双势阱问题.     

方阱势下的赝自旋劈裂和自旋劈裂

通过求解具有方阱势的径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋和自旋双重态的能级劈裂和波函数劈裂随着方阱势的势阱深度参数和势阱半径参数的变化关系, 此外, 能级劈裂和波函数劈裂随着量子数的变化关系也被进行了研究. 由于在特定的同位素链中, 势阱深度参数和势阱半径参数与核子数有关系, 所以以这些参数为变量对于赝自旋劈裂和自旋劈裂的研究是有意义的, 研究的结果至少可以定性的应用到大部分原子核中.     

一维有限深方势阱能量本征方程的泰勒级数解和二次近似解

一维有限深方势阱能量本征方程的求解受限于超越方程,无法严格求解.本文将奇、偶宇称情况的超越方程归结为一个方程,自洽地给出两种近似解析解：一阶泰勒级数解和二次近似解.分析二者适用范围并做误差分析,发现泰勒级数解可以很好地理解能谱随量子数n平方变化的数值解(即,所谓n平方律),但在特定参数R下失效,该参数正比于势阱宽度乘以势阱高度开方.二次近似解对所有参数R都适用,能谱在大R极限下,可退化为精确求解的无限深势阱情况.对于任意参数R,二次近似波函数的保真度始终大于99.7%.     

一维无限深梯形势阱中微观粒子波函数和能级的半解析解

利用特殊函数研究了一个数学形式简单但物理内涵丰富的新势阱——一维无限深梯形势阱,并得到了处于该势阱中微观粒子的波函数和能级的半解析解,其结果可以用来从理论上分析梯形沟道势阱的二维电子气的物理机制.此外指明了它与熟知的一维无限深方势阱和三角势阱的联系与区别,并基于对应原理讨论了该模型下粒子波函数的特征.     

Gross-Pitaevskii方程的数值解及其动力学研究

采用辛-打靶法求解了简谐势阱中碱金属玻色-爱因斯坦凝聚原子在T=0时的基态波函数,检验了波函数的稳定性,并研究了当简谐势阱突然改变时波函数随时间演化的动力学.     

势阱中粒子能级与波函数微扰计算的代数递推公式

利用超位力定理（HVT）和Hellmann-Feynman定理（HFT）,导出了由有精确解的势阱的能级值用微扰法直接计算一维势阱的各级近似能级的普遍代数公式,并导出由能级近似值计算定态波函数近似表达式的代数公式,给出了代数公式具体应用的几个典型一维势阱实例,此法可推广到二维势阱与三维势阱的情形。     

单粒子共振态的实稳定方法研究

基于实稳定方法的基本思想，在坐标空间求解了一维势阱和三维球对称势阱中的单粒子共振态，得到的共振能量、宽度和波函数等与散射相移法以及耦合常数的解析延拓方法的结果一致. 关键词： 共振态 实稳定方法 相移 共振宽度     

Hartmann势的Klein-Gordon方程束缚态解及递推关系

给出了在Hartmann型标量势与矢量势相等的条件下其Klein-Gordon方程束缚态解.结果表明 ，径向波函数可用广义Laguerre多项式表示，其角向波函数可用Legendre多项式表示.另外 ，给出了径向波函数关于角量子数l和量子数n的二类新递推关系. 关键词： Hartmann势 Klein-Gorgon方程 束缚态 递推关系     

二维氢原子径向方程的两种解法

本文利用两种方法求解二维氢原子的径向方程：一是升降算符法，由所定义的关于量子数ｍ的升降算符，给出了径向波函数之间的递推公式，求出了二维氢原子的能级和径向波函数的表达式；二是通过与三维氢原子径向方程的类比，在三维氢原子径向波函数的基础上，直接给出了二维氢原子径向波函数的一般表示式．两种解法所得结果完全一致．     

Exact hole-bound states for semiconductor quantum wells with arbitrary potential profiles

An efficient numerical-analytical method for finding confined and continuum states in quantum-well systems with arbitrary potential profiles, described by coupled Schrödinger equations, is presented. The method is based on the analytical properties of the wave functions, in particular, the power series representation of solutions of the corresponding coupled differential equations. Using only the general properties of the coefficients of a system of an arbitrary number of coupled Schrödinger equations, and imposing for definiteness the simplest boundary conditions, we derive exact expressions for the wave functions and present methods for accurate calculations of the energies and wave functions of confined states and of the wave functions of continuum states in quantum wells. The method is applied to the calculation of the dispersion of hole bound states in a single GaAs quantum well with truncated parabolic confining potentials of different strengths. The results are compared with data available from previous calculations.     

一维有限超晶格的电子态与透射问题的转移矩阵方法研究

采用转移矩阵方法,研究了一维有限超晶格的电子态与透射问题.计算了一维有限超晶格含单个缺陷层或少量缺陷层的透射谱和波函数,以及当电子被束缚在一维有限超晶格中电子的本征值和相应的定态本征函数.给出的方法对于研究电子通过任意排列的一维有限超晶格的输运具有普适性.     

Quantum well excitons in an electric field: two versus three dimensional behavior

Previous calculations have shown a transition between two dimensional and three dimensional behavior of excitons confined in a semiconducting quantum well structure as a function of electric field. We here present calculations of the exciton binding energy as a function of electric field using a two parameter variational wave function of the form used in the absence of the electric field by Matsuura and Shinozuka. Our calculations were performed using a finite potential barrier model for the confinement of the exciton in the quantum well. The results of our calculations confirm the validity of the conclusion that the variational exciton wave function goes from being of a purely 2D hydrogenic type at small well widths and/or low electric fields to a 3D hydrogenic type in wide wells and/or high electric fields.     

Nonlinear optical properties of asymmetric n-type double <Emphasis Type="Italic">δ</Emphasis>-doped GaAs quantum well under intense laser field

The effect of non-resonant intense laser field on the intersubband-related optical absorption coefficient and refractive index change in the asymmetric n-type double δ-doped GaAs quantum well is theoretically investigated. The confined energy levels and corresponding wave functions of this structure are calculated by solving the Schrödinger equation in the laser-dressed confinement potential within the framework of effective mass approximation. The optical responses are reported as a function of the δ-doped impurities density and the applied non-resonant intense laser field. Additionally, the calculated results also reveal that the non-resonant intense laser field can be used as a way to control the electronic and optical properties of the low dimensional semiconductor nano-structures.     

Polaron in a superlattice with δ-like potentials

The problem of the polaron spectrum is studied in a superlattice having narrow quantum wells and relatively wide potential barriers. A δ-like superlattice potential is chosen to solve the problem. This model is adequate, if the penetration depth of the electron wave function into the barrier region is much greater than the width of the quantum well. A weak-coupling polaron at low temperature is studied. Only volume phonons are considered. Expressions are obtained for the polaron mass and the shift of the polaron energy under these assumptions. To test the model, numerical calculations were performed for an InAs-GaSb superlattice, whose quantum wells are quite deep (the energy offset of the conduction bands in InAs and GaSb equals 830 meV), narrow (the width of a quantum well corresponds to the width of an InAs monolayer 6 Å), and the barrier width corresponding to the thickness of the GaSb layers equals 150 Å. The assumption that the penetration depth of the wave function is much greater than the barrier width holds well.     

Spin-orbit interaction in coupled quantum wells

We theoretically investigate the spin-orbit interaction in GaAs/AlxGa1 x As coupled quantum wells. We consider the contribution of the interface-related Rashba term as well as the linear and cubic Dresselhaus terms to the spin splitting. For the coupled quantum wells which bear an inherent structure inversion asymmetry, the same probability density distribution of electrons in the two step quantum wells results in a large spin splitting from the interface term. If the widths of the two step quantum wells are different, the electron probability density in the wider step quantum well is considerably higher than that in the narrower one, resulting in the decrease of the spin splitting from the interface term. The results also show that the spin splitting of the coupled quantum well is not significantly larger than that of a step quantum well.     

半无限深势阱中自旋相关玻色-爱因斯坦凝聚体的量子反射与干涉

玻色-爱因斯坦凝聚体与势垒或势阱的量子反射及干涉是考察宏观物质波奇特物性的最有效途径之一.利用传播子方法和基于冷原子实验广泛采用的飞行时间吸收成像方案,研究自旋相关玻色-爱因斯坦凝聚体在半无限深势阱中的反射和干涉演化动力学,得到了自旋相关的凝聚体波函数的严格解析解.结果表明,当自旋相关光晶格关闭后,非局域于不同格点中相同自旋态的物质波在自由膨胀过程中发生量子干涉,形成了对比度明显的干涉条纹.与此同时,扩张的自旋相关物质波包与半无限深势阱壁相遇发生量子反射,反射波与入射波产生二重干涉,在密度分布两边对称的局部位置出现剧烈的振荡,干涉条纹表现出显著的调制效应.分析讨论了自旋态、相干输运距离和相对相位等因素对干涉条纹的影响.该研究有助于促进对自旋相关凝聚体宏观量子特性的认识,为深入检验自旋相关光晶格中凝聚体干涉的理论模型和物理机理提供依据和新方案.     

Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

We study dynamical behaviors of a Bose-Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability R_s. Variation of the reflection probability with respect to the orientation angle θ of the dark soliton can be well described by a cosine function R_s~cos[λ(θ-π/2)], where λ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitive width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.     

Spatial imaging of two-dimensional electronic states in semiconductor quantum wells

We measure the spatial distribution of the local density of states (LDOS) at cleaved surfaces of InAs/GaSb isolated quantum wells and double quantum wells (DQWs) by low-temperature scanning tunneling spectroscopy. Distinct standing wave patterns of LDOS corresponding to subbands are observed. These LDOS patterns and subband energies agree remarkably well with simple calculations with tip-induced band bending. Furthermore, for the DQWs, coupling of electronic states between the quantum wells is also clearly observed.