低温下自旋为1/2的一维亚铁磁棱型链系统的元激发谱

利用不变本征算符法计算了低温下自旋为1/2的一维亚铁磁棱型链系统的元激发谱,并讨论了在此系统中不同的特殊情形下的元激发能量及不变本征算符法的优点与不足.     

外场与介观约瑟夫森结相互作用的不变本征算符法研究

本文首先详细介绍了场与介观约瑟夫森结相互作用系统的哈密顿量,进一步讨论了系统的量子化方案,然后简要介绍了不变本征算符法及其基本应用.在此基础上,用不变本征算符法求得外场与介观约瑟夫森结相互作用系统的能级间隔.     

低温下自旋为1/2的海森伯亚铁磁棱型链的1/3磁化平台

本文利用Jordan-Wigner变换和不变本征算符法计算了低温下自旋为1/2的海森伯亚铁磁棱型链系统的元激发谱,得到了三支没有简并的元激发谱.利用不变本征算符法对系统的哈密顿量进行了对角化,并导出有限温度和外磁场下的系统的配分函数及磁化强度.在绝对零度与有限温度下,通过分析诸交换积分(J1,J2,J3,Jm)对系统的磁化强度随外磁场的变化规律,得到了系统的三个临界磁场强度(HCB,HCE,HCS),并从三支元激发的性质说明了三个临界磁场强度起源及系统的磁化强度随外磁场变化出现1/3磁化平台的起因.     

三体耦合摆量子系统的精确波函数

利用不变本征算符法研究了三体耦合摆量子系统的简正频率及其对应的简正坐标与共轭动量,并对系统的哈密顿量进行了退耦合,得到了系统的明显的简正频率解析解.推导出在坐标表象中系统的精确波函数的解析解.但是,不变本征算符法对于计算系统哈密顿量中包含力学量的3次方及3次方以上的项时非常复杂.     

铁磁体的热力学性质

可将自旋算符S~a变换为自旋偏离算符b,如果将b看成玻色算符,可得到与自旋波理论相同的结果,此时由于忽略了自旋偏离不能超过2s的限制条件(因为玻色子的粒子数算符b~+b的本征值是所有的自然数),因而这种理论只适用于比居里点T_c低得多的温度范围。当温度升高,特别是在居里点附近,出现较大自旋偏离的几率增加,这时上述限制条件将起重要作用,自旋偏离算符b不能再看成是玻色算符。由此可见,要利用变换来讨论任意温度下的铁磁理论,首先必须导出自旋偏离算符b的严格对易关系。     

体积算符对任意价顶角的本征作用与本征值谱

利用体积算符所含抓三元组对自旋网任意价顶角中圈线作用的反称化和双元恒等式，证明了这种作用均为本征作用，本征值为-2.用代数方法给出了对任意价顶角求体积算符本征值的系统程式，得到了普遍情况下的3，4，5和6顶角体积本征值的具体代数表式. 关键词： 体积算符 任意价顶角 本征作用证明 本征值谱     

自旋结网圈表象中体积与面积本征值

利用抓算符作用的反称化和双元恒等式，通过计算，证明了3价和任意价自旋结网圈分别为体积和面积算符的本征态，并得到了体积本征值为2^-32l³₀∑ip_σp_τp_ρ和面积本征值为2^-1l²₀∑jp_l(j)的结果. 关键词： 体积算符 面积算符 本征值 自旋结网圈     

用不变本征算符法求一维线性谐振子的量子化能谱

采用不变本征算符法与积分变换法相当简捷地求出一维线性谐振子的量子化能谱.     

界面各向异性对双层铁磁薄膜自旋波性质的影响

在海森堡模型的基础上,采用界面参数化方法,将双层铁磁薄膜中自旋波本征值问题归结为联立求解能量约束方程和界面参数化方程.重点研究了界面各向异性对薄膜中自旋波本征问题的影响.结果表明:界面各向异性使对称模的波形在界面处呈现明显的钉扎现象,且界面模的能量随各向异性场增强而增大.     

第一类Poschl-Teller势的非线性代数结构

在形变李代数理论的基础上,利用哈密顿算符和自然算符,构造出第一类Poschl-Teller势的非线性谱生成代数。该非线性代数能够完全确定势场的能量本征态集合和本征值谱,在适当的非线性算符变换下可以化为谐振子代数,显示了该系统具有新的对称性。     

Energy Level of Coupled Harmonic Oscillator Model Born of Heisenberg Ferromagetic Spin Chain Derived by Invariant Eigen-operator Method

Based on the coupled harmonic oscillator model, which is born of Heisenberg ferromagnetic spin chain with nearest-neighbor interactions, we adopt the invariant eigen-operator method to derive its energy level, which provides an alternate approach to dealing with the dynamics of spin chain.     

Energy Level of Three-Mode Harmonic Oscillator for Coordinate Operators Satisfying Cyclic Commutative Relations Obtained by IEO Method

Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.     

Deriving Energy-Gap of Some Nonlinear Hamiltonians by Invariant Eigen-operator Method

By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for some Hamiltonians describing nonlinear processes in particle physics. In this way the energy-gap of the Hamiltonians can be naturally obtained. The characteristic polynomial theory has been fully employed in our derivation.     

Energy-Level of Some Singular Harmonic Oscillators and Parametric Amplifiers with Singular Potential Derived via IEO Method

We employ the invariant eigen-operator （lEO） method to find the invariant eigen-operators of N-body singular oscillators＇ Hamiltonians and then derive their energy gaps. The Hamiltonians of parametric amplifiers with singular potential are also discussed in this way.     

Solving Energy Levels for SSH Hamiltonian Describing Peierls Phase Transition by Virtue of Invariant Eigen-operator Method

We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.     

简正坐标的另一种求法

将不变本征算符方法推广到经典体系,并利用它来求体系的简正坐标.     

New approach for calculating the energy level of quantum harmonic oscillator with invariable energy gap

To overcome the difficulty of calculating the energy level of quantum harmonic oscillator via traditional method, we derive a new approach by using the normal ordering of the operator and the invariant eigen-operator. Based on this method, we find the energy level of singular harmonic oscillator.     

Dispersion Energy in a Molecule Composed of Two Anisotropic Vibrating Dipoles

For the first time, we derive the dispersion energy for a molecule which involves the anisotropic dipole interaction by virtue of the invariant eigen-operator method, which greatly simplifies the usual calculation if one uses the Schr(o)dinger equation.     

利用IEO方法求解多原子分子的振动能谱

对于线性多原子分子体系模型,借助从海森伯方程出发的不变本征算符(IEO)方法,很方便地求解了相应哈密顿量的本征能谱与振动频率,从而给出IEO方法在分子物理中的进一步应用.