均匀恒定磁场中带电狄拉克粒子的超对称性和本征能谱

基于狄拉克方程中γ矩阵有结构、可分解的观点, 把γ矩阵分解为自旋空间和正反粒子空间的算子的直积, 确定了均匀恒定磁场中带电狄拉克粒子的哈密顿量的动力学超对称性和可互易的完备的物理量算子集及其量子数集, 求得了用上述量子数完全集标志的该哈密顿量的解析的本征解,讨论了系统的哈密顿H的动力学超对称性中自旋对称性和正反粒子对称性破缺的不同情况,确定了自旋剩余超对称性导致的自旋简并子空间的超对称性变换群算子.     

幺正变换与二粒子耦合体系Hamilton量的对角化技术

本文给出耦合项为Ｂｉ（ａ１＾＋ａ２＾＋－ａ２ａ１）＋Ｃｉ（ａ１＾＋ａ２－ａ２＾＋ａ１）Ｈａｍｉｌｔｏｎ量的解耦合方法，可作为笔者在《大学物理》１９８９年第６期和１９９３年第５期上所发表的两篇文章的续篇。     

玻戈留玻夫变换与哈密顿量的对角化——兼与郭子政先生商榷

指出《大学物理》１９９５年第６期一中的错误，给出了将哈密顿量对角化问题转变成其系数矩阵本征值计算问题的条件。     

环状非有心球谐振子势场赝自旋对称性的三对角化表示

提出一个包含非有心电耦极矩势的环状谐振子模型,在能够负载波动算子三对角化矩阵表示的完全平方可积L2空间讨论了这一势场的赝自旋对称性．利用三对角化矩阵方案,给出了波函数角向分量和径向分量展开系数满足的三项递推关系式．角向波函数和径向波函数分别以Jacobi多项式和Laguerre多项式表示,由径向分量展开系数递推关系式的对角化条件得到束缚态的能量谱．并以Descartes多项式的符号法则讨论了能量方程的代数结构．     

哈密顿算符的对角化与能量本征值问题的代数解法

提出了将哈密顿算符对角化的一种方法.围绕一维谐振子讨论了如何将哈密顿算符对角化、引进的是玻色算符还是费米算符的问题,并分析了能量量子化的原因及能量子与声子的区别.     

单电子原子模型势中粒子的双波函数描述

运用双波函数量子理论,给出了单电子原子模型势中粒子的双波函数描述.结果表明运用双波函数描述的是单个粒子的运动,并将通常的量子力学描述结果作为系综统计平均值包含在其中.     

Os-Pt区核的基态三轴形状

在偶-偶核基态中寻找稳定的三轴形状,其中最大三轴形变为|γ|≈30°,仍然是核结构的一个主要主题。在本工作中,使用推转Woods-Saxon(WS)壳模型来研究Os-Pt区基态和集体转动态中可能的三轴形状。为寻找核态可能存在的三轴形变,具体用对力-形变-转动频率自洽推转壳模型对偶-偶^176-202Os和^182-204Pt同位素进行了总Routhian面计算。计算是在四极形变(β₂,γ)网格中进行的,而十六极形变β₄可变。事实上,在四极形变(β₂,γ)的每个网格点上,计算的能量相对于十六极形变β₄最小化。发现某些核的基态譬如¹⁹⁶Os和^188-194Pt既非扁椭球亦非长椭球,而是在这些核中基态极小值是形状非轴对称的,即三轴形变。同时,我们把从实验数据提取出的转动惯量与我们的计算结果作比较,显示实验数据不能很好地与转动假定相一致,说明有振动行为。此外,我们使用一种辅助的方法提取了平衡γ₀值,该值...     

奇A Tl核超形变的形状演化

利用粒子-转子模型研究了奇A Tl核yrast超形变核态的能谱,能量的旋称分离以及低自旋区的M1跃迁,理论值和实验值符合较好,研究表明奇A Tl超形变核态具有小的三轴形变,随着N的增加,重的Tl核比轻的Tl核四极形变要稍大.     

三维各向异性耦合谐振子体系的量子化能谱与精确波函数

利用二次型理论,通过三次保对易的辛变换,成功解决了三维各向异性耦合谐振子哈密顿量的对角化问题.进一步,给出了体系的量子化能谱和精确波函数.     

原子核的手证对称性

 手套有左右两只,ＤＮＡ有左旋右旋两种,许多分子也都有两个相互镜象对称的形式,通常称为左手形式和右手形式。现在,物理学家又发现原子核也有左手性和右手性两种模式。物理学家一直在寻找对称性和对称性破缺,从而揭示出基本的物理原理。最初,人们认为原子核是球形的,有着高度的对称性。后来实验发现原子核可以在很大程度上被拉长,甚至会像一支雪茄。20世纪60年代,理论物理学家预言原子核可以有三轴形变(即非轴对称形变)---对称性进一步降低,但是一直都没有被实验证实。     

Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators

We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in quantizing the system in this work. To this end, we first transform the invariant operator to a simple one by using a unitary operator in order that we can easily manage it. The invariant operator is further simplified through its diagonalization via three-dimensional rotations parameterized by three Euler angles. The coupling terms in the quantum invariant are eventually eliminated thanks to such a diagonalization. As a consequence, transformed quantum invariant is represented in terms of three independent simple harmonic oscillators which have unit masses. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators.     

n模二次型哈密顿量对角化的一种简单方法

利用线性量子变换理论，对ｎ模Ｂｏｓｅ（Ｆｅｒｍｉ）体系给出了一种简单的对角化方法。     

Modified Hill determinant approach to the eigenvalues of the anharmonic oscillator

The unperturbed Hamiltonian of quantum anharmonic oscillator is modified by introducing a simple variational scale parameter. A suitable choice of this parameter makes the eigenvalues rapidly convergent for small size of the determinant in the method of infinite Hill determinant. Simple analytic expressions for the eigenvalues are obtained by matrix diagonalization method.     

Projected total energy surface description for axial shape asymmetry in 172W

The projected total energy surface(PTES)approach has been developed based on the triaxial projected shell model(TPSM)hybridized with the macroscopic–microscopic method.The total energy of an atomic nucleus is decomposed into macroscopic,microscopic and rotational terms.The macroscopic and microscopic components are described with the liquid drop model and Strutinsky method,respectively,and the rotational energy is given by the TPSM,the term beyond the mean field.To test theory,the PTES calculations have been carried out for the yrast states of the well deformed rare earth nucleus172W,and the theoretical results are in good agreement with the experimental data.By using the equilibrium quardrupole deformations(ε2andγ)determined by the PTES,the calculation of the transition quardrupole moment(Qt)in function of spin also reproduces the experimental data.A comparison between the PTES and TRS methods has been made for theoretical and application uses.     

奇异拉氏量系统的正则对称性和Ward恒等式

给出了场论中约束Hamilton系统规范生成元的构成,说明了生成元中与第一类约束相联系的系数之间的关系.基于相空间中的生成泛函,导出了相应正则形式的Ward恒等式.讨论了与混合陈-Simons拉氏量等价的场论模型中的应用.     

Effects of single particle on shape phase transitions and phase coexistence in odd-even nuclei

A classical analysis of shape phase transitions and phase coexistence in odd-even nuclei has been performed in the framework of the interacting boson-fermion model. The results indicate that the effects of a single particle may influence different types of transitions in different ways. Especially, it is revealed that phase coexistence can clearly emerge in the critical region and thus be taken as a indicator of the shape phase transitions in odd-even nuclei.     

Simultaneous measurements of the release of atomic sodium, particle diameter and particle temperature for a single burning coal particle

The temporal history of the release of volatile alkali species during coal combustion is a significant, but poorly understood factor in the fouling and corrosion of heat transfer surfaces within industrial coal-fired boilers. We present new results of the simultaneous measurement of particle temperature, particle size and the atomic sodium concentration in the plume of a burning coal particle. During the char phase, the sodium concentration in the plume was found to be linearly dependent on the inverse of particle diameter, but during the ash phase the sodium concentration was found to decay exponentially with decreasing particle temperature. The centreline decay of Na within the plume above the burning particle consists of one region controlled by a first order chemical reaction and a second region controlled by diffusion.