第一类P?schl-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P?schl-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 关键词： P?schl-Teller势 自然算符 非线性谱生成代数     

第一类PschlTeller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P schl 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     

无限深阱势的非线性谱生成代数与新型相干态

利用对称一维无限深阱势的哈密顿算符和自然算符构造出该势场的非线性谱生成代数,并在此基础上得到了一种新的非线性相干态.该相干态具有时间稳定性,既可以看成本征值为算符函数的降算符本征态,也可以看成广义极小测不准状态的转动态.     

对称Pschl-Teller势的非线性谱生成代数

利用哈密顿和自然算符,构造出对称Poschl-Teller势的非线性谱生成代数,给出了一种描述和求解微观粒子运动的具有明显物理意义的新代数方法．当参数趋于零时,该代数成为振子代数,因而又可以看成是后者的一种新的非线性形变．     

对称Pschl-Teller势的非线性谱生成代数

利用哈密顿和自然算符,构造出对称Poschl–Teller势的非线性谱生成代数,给出了一种描述和求解微观粒子运动的具有明显物理意义的新代数方法.当参数趋于零时,该代数成为振子代数,因而又可以看成是后者的一种新的非线性形变.     

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     

用不变量方法解具有非线性场和原子与场非线性耦合的Jaynes-Cummings模型

采用Lewis-Riesenfeld不变量方法研究了具有非线性场和任意形式原子与场相互作用的Jaynes-Cummings模型.该模型由于具有超对称代数结构,因此其Hamiltonian量可用超对称算符的线性组合表示.在算符N′的本征值子空间,用生成元算符构造出系统的不变量后,利用不变量方法求得了系统的一般波函数和时间演化算符,同时也计算了原子布居数和光子数的时间演化表达式.     

~(40)Ca区域原子核的单粒子和单空穴谱

应用由单粒子格林函数导出的本征方程,严格顾及G矩阵的偏离能壳性,得到的~(39)Ca单空穴谱和~(41)Ca单粒子谱与实验值符合颇好,其中~(41)Ca的单粒子谱较以往的RBHF结果有明显改进。取含有能移的等效谐振子表象作为初始近似,计算了单粒位阱u_(αβ)=M_(αβ)(ε_β)(M_(αβ)(ω)表示质量算符)的本征解,亦得到颇好结果。此外,本文还考查了G矩阵中泡利算符的选取及谐振子能量零点的选取对能谱的影响。比较Reid软心势与Paris势的计算结果表明Paris势是一个较好的核力势。     

在局域子空间中计算给定范围内的能量本征值

通过能量算符δ函数作用于完全随机格点波函数,构造了可用于直接计算给定范围[Emin,Emax]内能量本征值和本征函数的局域子空间.在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示,讨论了广义本征值问题的解法.以Morse势和Henon-Heiles势的多个能量范围为例检验了算法     

不变本征算符方法求解含不同在位势的一维双原子链的色散关系

本文运用全量子化的不变本征算符方法, 求解了含有不同简谐在位势的一维双原子链模型, 得到其色散关系并讨论了不同在位势系数之比和力常数对于色散关系高频支和低频支的影响, 分析发现在位势的存在使得低频支和高频支的频谱都有一定程度的抬高; 在一定的条件下, 布里渊区边界的高频支与低频支存在交点, 意味着在某些在位势下, 高频支与低频支的频隙为零. 关键词： 在位势 一维双原子链 不变本征算符方法 色散关系     

Nonlinear Deformed Algebra Realized in a Physical System

We show that nonlinear deformed algebra can exist in a physical system with Poschl-Teller potential. Due to this algebra, the eigenvalue problem of the system can be exactly solved by operator method. The raising and lowering operators satisfying this algebra are constructed. And the physical meaning of two deforming functions involving in this algebra is given. In addition, the SU(1,1) symmetry is exhibited in such a system by the operator method.     

Nonlinear Spectrum and Generating Algebra for Infinitely Deep Square Well Potential and New Coherent State

Using the Hamiltonian of symmetrical one dimersional infinitely deep square well potential and natural operators,we obtain its nonlinear spectrum and generating algebra,and get a class of new nonlinear coherent states on the basis of the nonlinear algebra obfained. These coherent states are of temporal stability,and can be regarded as the eigenstates of the lower operator with the eigenvalues in an operator field and as the rotational states of the generalized minimal uncertainly states as well.     

Nonperturbative Operator Quantization of Strongly Nonlinear Fields

At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of a strongly nonlinear field can form a non-associative algebra. It is shown that such an algebra can be described as an algebra of some pairs. The comparison of presented techniques with the Green's functions method in superconductivity theory is made. A possible application to the QCD and High-T _c superconductivity theory is discussed.     

ONEOptimal:A Maple Package for Generating One-Dimensional Optimal System of Finite Dimensional Lie Algebra

We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver＇s theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.     

Lax表示的Kac—Moody代数结构

本文指出,非线性(演化)系统的广义Lax表示所取值的代数,即延拓代数y×D(λ),实质上是Kac-Moody代数。这里,y是一有限维李代数,D(λ)是谱参数λ的值域。本文并利用Dolan关于主手征模型Kac-Moody代数的实现,给出了一类1+1维非线性(演化)系统的Kac-Moody代数的实现。 关键词：     

Algebra of charges in the supersymmetric nonlinear σ model

We examine the algebra of the nonlocal charges in the supersymmetric nonlinear σ model and show that they satisfy a nonlinear algebra at the tree-level. We also discuss other interesting questions like the transformation of these charges under a supersymmetry transformation and speculate that this algebra possibly continues to hold in the full quantum theory.     

Generalized Multi-component TC Hierarchy and Its Multi-component Integrable Coupling System

A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1.It follows that a generalscheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally,an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach.