等价电子耦合波函数的构造和矩阵元计算

按(U,D)L-LSQ-R耦合格式构造等价电子耦合波函数(这里U(D)是自旋向上(向下)电子的轨道角动量,Q是准旋,R是自旋-准旋交换算符),只需对半满壳层计算耦合波函数,其它电子数耦合波函数可通过准旋升、降算符和自旋-准旋交换算符的作用得到.对p,d,f,g壳层进行了耦合波函数和产生-湮没算符约化矩阵元计算.理论分析和实际计算表明,(U,D)L-LSQ-R耦合格式比一般LS耦合格式更便于计算. 关键词：     

同调谐振子参数与基态能量的关系

采用升降算符方法研究了同调谐振子(包括一维谐振子)定态薛定谔方程的严格解,详细讨论了谐振子参量不同取值范围形成不同基态能量的关系.对于有关文献的一些欠完善的提法给予了分析和澄清 关键词： 同调谐振子 升算符 降算符 基态能量     

标量算符本征值对g壳层LSQ耦合态的完全分类计算

按（Ｕ,Ｄ）Ｌ－ＬＳＱ格式构造ｌ壳层ＬＳＱ耦合态,这里Ｕ（Ｄ）是自旋向上（向下）电子的轨道角动量,Ｌ、Ｓ、Ｑ是总轨道角动量、总自旋和准旋。由４个产生－湮灭算符构造与轨道、自旋准旋算符均为易的标量算符并用基本征值对ＬＳＱ耦合态进上步分类,实现了对ｆ、ｇ壳层耦合态的完全分类,列出了ｇ壳层耦合态完全分类的主要结果。     

Rashba自旋-轨道相互作用对一维谐振子势场中电子性质的影响

分析了Rashba自旋-轨道相互作用对一维谐振子势场中电子性质的影响,发现该自旋-轨道相互作用能够导致能级之间的自旋翻转,并且自旋翻转的性质明显依赖于自旋-轨道耦合系数和参考系坐标之间的关系.     

求解三模耦合谐振子精确能谱的一种方法

基于相空间中的幺正转动变换,利用有序算符内的积分技术,得到了相空间中转动算符、傅里叶变换算符和宇称算符的相干态表示.进而引入并利用相空间中的三模转动算符,简捷地实现了三模坐标-动量耦合谐振子哈密顿量的退耦合,给出了该耦合形式谐振子的精确能谱及其能量本征态.     

量子力学中对称性和阶梯算符

本文讨论了自由粒子、库仑场和谐振子场的对称性和相应的阶梯算符的关系．从体系对称群的无穷小算符得到了自由粒子、库仑场中的电子及谐根子在坐标表象中的径向升、降算符，并由体系的对称性说明了通常的径向阶梯解法中不同形式的阶梯算符的统一性．指出寻找阶梯算符的途径：体系的对称性→对称变换（幺正变换）无穷小生成算符→阶梯算符。     

Fe_2P_2S_6晶体基态能级的精细结构及其Jahn-Teller效应的研究

在弱场图像下,利用Racah不可约张量算符方法得到了三角对称3d4/3d6电子组态的完整的哈密顿矩阵。研究了Fe2P2S6晶体中Fe2+的基态能级和晶体结构,考虑了自旋-轨道耦合与自旋-自旋耦合对基态能级的影响,对Fe2P2S6晶体基态能级和电子顺磁共振的零场分裂进行了计算。计算结果与实验值符合得较好。基于此计算结果,对基态能级和零场分裂中的自旋-轨道耦合、自旋-自旋耦合以及3 L低自旋态进行了更深入的研究,并对Fe2P2S6晶体的Jahn-Teller效应进行了研究。     

描述自旋体系密度算符演化的新方法

提出一种描述自旋体系密度算符演化的新方法,可统一处理核磁共振波谱学中强、弱偶合自旋体系及弱射频场存在下密度算符的演化。具体分析一些核磁共振实验:自旋轻扰、自旋锁定、偶极耦合作用、强耦合AB和ABX自旋体系的演化。     

电子自旋是角动量的讨论

从施特恩-盖拉赫实验测量的结果电子自旋只有两种取值出发,在不引入自旋算符的具体矩阵表示的情况下,利用矩阵求迹,导出自旋算符和轨道角动量算符满足完全相同的对易关系,从而说明自旋与轨道角动量同类,属于角动量.区别于历史上和国内外量子力学教材中直接将自旋归为角动量,本文尝试用"物以类聚"的逻辑对自旋是角动量进行讨论.     

两体自旋轨道耦合力与f7/2壳层能谱

本文采用中心力加两体自旋轨道耦合力作为剩余相互作用,计算了 f_7/2壳层原子核的能谱.交换参数可调.径向波函数采用谐振子波函数.计算值和实验值的符合程度令人满意.因而表明在剩余相互作用中,两体自旋轨道相互作用的影响不可忽视.     

Pseudospin symmetry and the relativistic ring-shaped non-spherical harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The eigenfunctions and eigenenergies are obtained for the ring-shaped non-spherical harmonic oscillator by solving Dirac equation with equal mixture of vector and scalar potentials in opposite signs, for which pseudospin symmetry is exact. Several particular cases such as the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

Wave function of the harmonic oscillator in classical statistical mechanics

The notion of wave function of the classical harmonic oscillator is discussed. The evolution equation for this wave function is obtained using the classical Liouville equation for the probability-distribution function of the harmonic oscillator. The tomographic-probability distribution of the classical oscillator is studied. Examples of the ground-like state and the coherent state of the classical harmonic oscillator are considered.     

Behavioral Differences of a Time-Dependent Harmonic Oscillator in Commutative Space and Non-Commutative Phase Space

In this article, behavioral differences of time-dependent harmonic oscillator in Commutative space and Non-Commutative phase space have been investigated. The considered harmonic oscillator has a time-dependent angular frequency and mass which are function of time. First, the time-dependent harmonic oscillator is studied in commutative space, then similar calculation is done for considered harmonic oscillator in Non-Commutative phase space. During this article method of Lewis–Riesenfeld dynamical invariant has been employed.     

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

Power Series Expansion of Propagator for Path Integral and Its Applications

In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

Coupling of the relaxation and resonant elements in the autonomous chaotic relaxation oscillator (ACRO)

If a harmonic oscillator is embedded in a relaxation oscillator, the resulting system may behave like an autonomous chaotic relaxation oscillator (ACRO). The discharge transient of the relaxation oscillator excites sinusoidal oscillations in the harmonic oscillator and these sinusoids affect when the next discharge occurs. This can lead to chaotic intervals in the oscillator periods. A simple electronic model of the ACRO is studied over a wide range of parameters using numerical, analytic, and experimental techniques. The dynamics of the ACRO is found to be determined by three parameters: (1) tuning, (2) coupling, and (3) damping. Complex, intermittent outputs can always be inhibited by increasing the damping of the harmonic oscillator. For weak damping, strong coupling yields chaotic periods. With weak damping and weak coupling, complex behavior only occurs if the relaxation oscillator is tuned near a resonance of the harmonic oscillator. A new path to chaos, called a disruption bifurcation, is the source for intermittency in the ACRO. This bifurcation occurs when the amplitude of internal resonances is excited to the degree that existing limit cycles are disrupted.     

Quantum harmonic oscillator with time-dependent mass and frequency

The quantum harmonic oscillator with time-dependent mass and frequency is analyzed by using the canonical transformation method. The varying mass and frequency of the system are reduced to constant mass and frequency, and the corresponding eigenvalues and eigenvectors are derived. The exact time-dependent coherent state of the harmonic oscillator is constructed and shown to be equivalent to the squeezed state. Damped harmonic oscillators with different frictions and forced time-dependent harmonic oscillators are also discussed.     

二维各向同性变频率谐振子的超对称性及其不变量的超对称量子力学精确解

采用超对称量子力学与不变量相结合的方法讨论了二维各向同性变频率谐振子,给出了二维各向同性变频率谐振子的不变量,采用超对称量子力学方法精确求解了不变量的本征值和本征函数,并且给出了当频率恒定时,二维常频率谐振子的本征值和本征函数的精确解.最后对不变量的超对称性进行了讨论.     

Notes on Application of WKB Method

The notes here presented are of the modifications introduced in the application of WKB method. The problems of two- and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulation of quantization rule respectively. It is found that the energy spectrum of the radial harmonic oscillator, which is reproduced exactly by the standard WKB method with the Langer modification, is also reproduced exactly without the Langer modification via the new quantization rule approach. An alternative way to obtain the non-integral Maslov index for three-dimensional harmonic oscillator is proposed.