利用不变量本征算符求解二维耦合量子谐振子的能级间隔

目前不变量本征算符方法已成功地解决了某些量子系统哈密顿量能级问题.对于二维耦合量子谐振子,利用这一方法可以非常简捷有效地给出其能级信息,而不需要使其哈密顿量对角化.计算结果表明,不同耦合形式的二维耦合量子谐振子的能级间隔是不同的.     

单核子在具有八极形变的平均势场中的混沌运动(Ⅲ)初始相干态空时演化中几率密度及扰动强度的研究

运用在二维不对称谐振子势加八极形变势中传播的二维不对称谐振子相干态,研究了不同强度耦合作用下密度矩阵的复杂性及对干扰动强度微小变动的敏感性。发现相应于对应经典系统作规则、部分混沌、及整体混沌运动的相空间区域,量子系统有对应的特征性的表现,它们与势能面上负曲率的存在及负曲率的大小有关系.     

有限深抛物势量子环类氢杂质能级

在有效质量近似下,用微扰法研究InAs量子环内类氢杂质基态及低激发态的能级.受限势采用有限深抛物型势,在二维平面极坐标下,用薛定谔方程的解析解计算.数值结果显示:在抛物势平台区,类氢杂质能级不随电子径向坐标改变,并具有二维氢原子能级的特征;在有限深抛物势区,电子能级敏感地依赖于量子环半径,能级存在极小值,这是由于限制势采用抛物势的结果.如果减小环的半径,可以增加能级间距;简并能级发生分裂并且间距随半径增大而增大,第一激发态的简并没有消除,第二激发态的简并被部分地消除.本文结果对研究量子环的光跃迁及光谱结构有指导意义.     

InAs量子环中类氢杂质能级

在有效质量近似下,利用微扰法研究了InAs量子环内类氢杂质基态及低激发态的能级分布.受限势采用抛物形势,在二维平面极坐标下,用薛定谔方程的精确解析解进行计算.数值计算结果显示,电子能级敏感地依赖于量子环半径,能级存在极小值,这是由于限制势采用抛物势的结果.如果减小环的半径,可以增加能级间距.第一激发态类氢杂质能级的简并没有消除,n≥2时简并的能级发生分裂并且间距随半径的增大而增大.电子能级间距还敏感地依赖于角频率并随角频率的增大而增大.第一激发态的简并没有消除,第二激发态的简并被部分地消除.在计算InAs量子环中类氢杂质的基态和低激发态的能级时,角频率改变的影响也是很深刻的.文章结果对研究量子环的光跃迁及光谱结构有重要指导意义.     

在磁场作用下含有杂质的半导体量子环中电子的能级

由于量子环特殊的结构,我们尝试过不少方法,发现一般传统方法很难求解薛定谔方程,故很难求出它的波函数和能级。国内外很多学者从事这方面的研究,但发表的文献非常少。有必要寻找一些新的方法从事这方面的研究工作,本文中采用了B样条函数近似拟合波函数的方法,计算了一个在谐振子束缚势和磁场作用下含有杂质的二维量子环中的电子能级。研究了电子能级随磁场强度、束缚势的变化关系以及电子能级与量子环半径的关系。我们发现电子能级随磁场强度、束缚势强度的增强而增强;每一个能级都有一个最小值在特定的量子环半径上,并且随着能级的增加,最小值的位置向半径大的方向偏移。     

单核子在具有八极形变的平均势场中的混沌运动（III）初始？…

运用在二维不对称谐振子势加八极形变势中传播的二维不对称谐振子相干态，研究了不同强度耦合作用下密度矩阵的复杂性及对于扰动强度微小动的敏感性。发现相应于应经典系统作规则、部分混沌、及整体混沌运动的相空间区域，量子系统有对应的特征性的表现，它们与势能面上负曲率的存在及负曲率的大小有关系。     

单核子在具有八极形变的平均势场中的混沌运动(Ⅱ)初始相干态空时演化中正则变量的期望值和测不准度的特征

研究了二维不对称谐振子的相干态在附加八极形变势作用下传播时,量子正则变量的期望值和测不准度的变化,发现量子混沌与相应的经典混沌完全对应地表现了多种性质.量子混沌的特征也与势能面的几何对称性,即势能面上负曲率的存在及负曲率的大小有关系.     

掌握概念,灵活运用——一道量子力学考研题的启示

 在量子力学中,3维各向同性谐振子是一个重要模型,它一共涉及了两个主要问题,一是能级简并度,二是在直角坐标系中的解法。其中能级简并度的重要性体现得尤为明显,因为与1维谐振子相比,相邻两能级的间距同样为w,但不同的是,3维各项同性谐振子的能级一般是简并的.     

二维各向异性谐振子的第三个独立守恒量及其对称性

二维各向异性谐振子和两分振子的能量是守恒的, 但三个守恒量中只有其中两个是独立的. 当频率比ω₁/ω₂ 为有理数时, 系统存在第三个独立的守恒量.本文用扩展Prelle-Singer 法得到五个典型谐振子的第三个独立守恒量, 并讨论了与守恒量相应的Noether对称性与Lie对称性.     

二维环状δ势的束缚态

讨论了二维自由空间和各向同性谐振子势下环状δ势束缚态波函数的表示,发现波函数由合流超几何函数和屈科米函数表示.由波函数在边界的衔接条件,得到了能谱方程,并给出了一定条件下前5个能级的数值解.     

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm(AB) flux fields on the energy levels of a two-dimensional(2D) Klein-Gordon(KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator(PHO).We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter,magnetic field strength,AB flux field,and magnetic quantum number by means of the Nikiforov-Uvarov(NU) method.The non-relativistic limit,PHO,and harmonic oscillator solutions in the existence and absence of external fields are also obtained.     

Aharonov-Bohm effect in spherical billiard

Using Gutzwiller's periodic orbit theory, we study the quantum level density of a spherical billiard in the presence of a magnetic flux line added at its center, especially discuss the influence of the magnetic flux strength on the quantum level density. The Fourier transformed quantum level density of this system has allowed direct comparison between peaks in the level density and the length of the periodic orbits. For particular magnetic flux strength, the amplitude of the peaks in the level density decreased and some of the peaks disappeared. This result suggests that Aharonov-Bohm effect manifests itself through the cancellation of periodic orbits. This phenomenon will provide a new experimental testing ground for exploring Aharonov-Bohm effect.     

Exact analytical results for density profile in Fourier space and elastic scattering function of a rotating harmonically confined ultra-cold Fermi gas

In this paper, the system dealt with consisting of an ultra-cold neutral spin-polarized Fermi gas undergoing rotation (or in the so-called synthetic magnetic field) trapped by an anisotropic harmonic potential in a two and three-dimensional space at zero temperature. Using the so-called Bloch propagator as a tool, we derive exact closed-form expressions for particle density in Fourier space which are valid for an arbitrary particle number confined by a two and three-dimensional rotating anisotropic harmonic trap. Numerical illustrations and discussions are presented. The results can be easily generalized at finite temperatures. The crossover from two-dimensional to the one-dimensional regime is shown to be reflected in the shape of the density distribution in Fourier space at very fast rotating velocity (or at strong synthetic magnetic field). In addition, an exact analytical expression of the elastic scattering factor is found, a quantity of interest used to probe the spatial distribution of the quantum gases.     

量子棒中弱耦合磁极化子的性质

给出了具有椭球边界量子棒经过坐标变换成球形边界的哈密顿量.采用线性组合算符和幺正变换的方法研究了在抛物限制势下量子棒中弱耦合磁极化子的振动频率和基态结合能随横向和纵向有效受限长度、电子-声子耦合强度、椭球的纵横比以及磁场的回旋频率的变化关系.数值计算结果表明:振动频率和基态结合能随回旋频率的增加而增大,随横向和纵向有效受限长度的减少而迅速增大.基态结合能随耦合强度的增加而增大.振动频率随纵横比的增加而减少.当e′1时,基态结合能随纵横比的增加而增加.e′1时,随着纵横比的减少,基态结合能增大.当e′=1时,基态结合能取稳定的极小值.     

A quantum pseudodot system with two-dimensional pseudoharmonic oscillator in external magnetic and Aharonov-Bohm fields

Using the Nikiforov–Uvarov (NU) method, the energy levels and the wave functions of an electron confined in a two-dimensional (2D) pseudoharmonic quantum dot are calculated under the influence of temperature and an external magnetic field inside dot and Aharonov–Bohm (AB) field inside a pseudodot. The exact solutions for energy eigenvalues and wave functions are computed as functions of the chemical potential parameters, applied magnetic field strength, AB flux field, magnetic quantum number and temperature. Analytical expression for the light interband absorption coefficient and absorption threshold frequency are found as functions of applied magnetic field and geometrical size of quantum pseudodot. The temperature dependence energy levels for GaAs semiconductor are also calculated.     

Electronic properties of a quantum ring perturbed with a quantum well in the presence of perpendicular magnetic flux

Here, we study the effects of the number of sites, quantum ring radius and potential well depth on the energy levels, persistent current, magnetic susceptibility and density of states (DOS) of a quantum ring with a quantum well within its circumstance in a magnetic flux perpendicular to its plane. We show that, for small radius quantum ring systems, there are periodic local gaps along the magnetic flux axis in the DOS plots and along the axis ‘energy’. For large radius quantum ring systems, a uniform gap along the energy axis exists and along the phi axis nothing changes. In quantum rings with a quantum well in their circumstance, by using the large confining potential, we can create uniform gaps in the Energy–phi plane. The energy eigenvalues, persistent current and magnetic susceptibility decrease by increasing the confining potential. A quantum ring even with a very small confining potential in its circumstance can sensibly decrease the persistent current and magnetic susceptibility, although it may do not change the energy eigenvalues and DOS maximum considerably. Thus, by using the abovementioned parameters, we are able to tune the DOS, persistent current, magnetic susceptibility and energy levels, desirably.     

A quantum pseudodot system with a two-dimensional pseudoharmonic potential

We investigate the energy spectrum and the corresponding wave functions of an electron confined by a pseudoharmonic potential both including harmonic dot and antidot potentials in the presence of a strong magnetic field together with an Aharonov-Bohm flux field. Exact solutions for the energy levels and wave functions are found for this exactly soluble system. These are all tested under various conditions and also are compared with other works found in the literature. Further, we discuss the related energy spectrum in terms of special values of the proposed pseudoharmonic potential, AB field and magnetic field as a function of magnetic quantum number and magnetic field.     

Two-electron quantum dot in tilted magnetic fields: Sensitivity to the confinement model

Semiconductor quantum dots are conventionally treated within the effective-mass approximation and a harmonic model potential in the two-dimensional plane for the electron confinement. The validity of this approach depends on the type of the quantum-dot device as well as on the number of electrons confined in the system. Accurate modeling is particularly demanding in the few-particle regime, where screening effects are diminished and thus the system boundaries may have a considerable effect on the confining potential. Here we solve the numerically exact two-electron states in both harmonic and hard-wall model quantum dots subjected to tilted magnetic fields. Our numerical results enable direct comparison against experimental singlet-triplet energy splittings. Our analysis shows that hard and soft wall models produce qualitatively different results for quantum dots exposed to tilted magnetic fields. Hence, we are able to address the sensitivity of the two-body phenomena to the modeling, which is of high importance in realistic spin-qubit design.     

Effect of a magnetic flux line on the quantum beats in the Henon-Heiles level density

The quantum density of states of the Henon-Heiles potential displays a pronounced beating pattern. This has been explained by the interference of three isolated classical periodic orbits with nearby actions and periods. A singular magnetic flux line, passing through the origin, drastically alters the beats even though the classical Lagrangian equations of motion remain unchanged. Some of the changes can be easily understood in terms of the Aharonov-Bohm effect. However, we find that the standard periodic orbit theory does not reproduce the diffraction-like quantum effects on those classical orbits which intersect the singular flux line, and argue that corrections of relative order variant Planck's over 2pi are necessary to describe these effects. We also discuss the changes in the distribution of nearest-neighbor spacings in the eigenvalue spectrum, brought about by the flux line. (c) 1995 American Institute of Physics.     

Dirac bound states of anharmonic oscillator in external fields

We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method.