玻戈留玻夫变换用于哈密顿对角化时的一种简化方法

玻戈留玻夫变换用于哈密顿量对角化时一般须首先直接或间接确定变换矩阵本身，通常比较繁琐本文在将哈密顿形式地写成矩阵之后，将哈密顿量对角化问题转变成其系数矩阵的本征值计算问题，这样不具体计算变换矩阵即可方便地实现对角化．     

氦原子~1S~e态的分波分析和强径——角关联区

氦原子的哈密顿量在四个空间的并空间内被对角化从而得到诸~1S~e态的解。对波函数进行了仔细的分析,找出了内部结构的一些特征。     

广义n维耦合谐振子体系的代数解法

利用二次型理论,通过三次保对易线性变换,实现了广义n维耦合谐振子体系哈密顿量的退耦合, 得到了体系对角化后的哈密顿量,并给出了体系的能量本征值和本征函数.     

关于二次型哈密顿量的对角化定理

众所周知,变换是处理多体问题常用的有力工具.对于玻色系统,它的含意已由的关于玻色二次型哈密顿量的对角化定理所确立.戴显熹将的讨论推广到费米系统,给出了类似的定理.但文献[2]关于费米二次型哈密顿量对角化的表达式有一点错误。另外,由于在过去的定理表述中某些方面没有确切地指出,常引起一些困惑.鉴于这个定理的重要性,为便于直接而确切地引用,也便于把文献中出现的多种情况纳入统一的框架,现将二次型哈密顿量对角化定理再表述和补充如下.     

利用表象变换精确求解最一般双耦合谐振子的能量本征值

将变换后的哈密顿量进一步变换到占有数表象,使哈密顿量对角化,精确求解出最一般双耦合谐振子,即哈密顿量中含非对角项(-λx1x2 vp1p2)的玻色谐振子的能量本征值．讨论了由耦合所引起的能级分裂。     

用超对称幺正变换解双光子过程的Jaynes-Cummings模型

本文发现了描写双光子过程的Jaynes-Cummings哈密顿量的超对称结构.根据超对称量子力学理论,引入了超对称幺正变换使其哈密顿量对角化.从而,得到了它的本征值、本征态,同时也计算了态的演化和跃迁几率.     

费米二次型哈密顿的对角化定理

本文分析了多体统计理论与能带理论相结合的重要性和实际需要,指出外场中超导体或计及晶格结构的超导体的哈密顿量,在适当的物理近似下,都可以归结为费米二次型的哈密顿量.为了这方面的需要,本文建立了同时适用于费米体系的二次型哈密顿的对角化定理,它是人们所熟知的的关于玻色二次型哈密顿的对角化定理的自然推广.     

压缩真空态的激发态下介观耦合电路的量子效应

通过量子化电容耦合电路和对角化电路哈密顿量,研究了介观电路在压缩真空态的激发态下的量子力学效应.     

氦原子1Se态的分波分析和强径——角关联区

氦原子的哈密顿量在四个空间的并空间内被对角化从而得到诸¹S^e态的解。对波函数进行了仔细的分析,找出了内部结构的一些特征。 关键词：     

三个非全同耦合谐振子哈密顿量的退耦合

对于哈密顿量为H＝∑^3i=11/2miP^2i 1/2k1(q2-q1-q0)^2 1/2k2(q3-q2-q0)^2的三个非全同耦合振子，我们打到一个方法使其对角化，给出了体系坐标和动量的变换式。     

Fermion Coherence Hamiltonians

We have established that the most general form of Hamiltonian that preserves fermionic coherent states stable in time, is that of the nonstationary free fermionic oscillator. This is to be compared with the earlier result of boson coherence Hamiltonian, which is of the more general form of the nonstationary forced bosonic oscillator. If however one admits Grassmann variables as Hamiltonian parameters then the coherence Hamiltonian takes again the form of (Grassmannian fermionic) forced oscillator.     

Generally Covariant Dirac Hamiltonian

The generally covariant Dirac equation reduces to a mathematically simple form with a clear physical meaning that is best demonstrated by the Hamiltonian formalism. The resulting Hamiltonian is compared to the corresponding classical Hamiltonian, and assumes a particularly simple form for the Robertson-Walker metric of the Standard Cosmological Model when that metric is expressed in a coordinate system referred to as Einstein coordinates because it is based on a coordinate constraint recommended by Einstein in his original paper on general relativity. A kinematic definition of distance, based on the form of the classical Hamiltonian, is used in discussing the physical meaning of the results.     

Symmetrized Hamiltonian versus ‘Foreman’ Hamiltonian for semiconductor valence band: an insight

A quantitative comparison of different k·p calculations of valence-band states in quantum-confined semiconductor heterostructures is presented. The importance of using the appropriate Hamiltonian form is studied quantitatively following a numerical method which enables discrimination between existing Hamiltonians. The correct form of the Hamiltonian appears to be the Foreman Hamiltonian, which gives physically reasonable results contrary to the symmetrized Hamiltonian.     

Geometry of quadrilateral nets: Second Hamiltonian form

Discrete Darboux–Manakov–Zakharov systems possess two distinct Hamiltonian forms (by this term we mean that equations of motion are discrete time extensions of Hamiltonian equations of motion). In the framework of discrete-differential geometry one Hamiltonian form appears in a geometry of a circular net. In this paper a geometry of the second form is identified.     

哈密顿Ermakov系统的形式不变性

把形式不变性的方法用于研究哈密顿Ermakov系统，从哈密顿Ermakov系统的形式不变性出发，运用比较系数法得到与形式不变性相应的点对称变换生成元的表达式及势能所满足的偏微分方程.结果表明，在点对称变换下，只有自治的哈密顿Ermakov系统才具有形式不变性. 关键词： 哈密顿Ermakov系统 拉格朗日函数 点对称变换 形式不变性     

Invariant combinations of coefficients in the rotational Hamiltonian

A general development of combinations of parameters in the asymmetric rotor Hamiltonian, which are independent of the coefficients of the contact transformation operators used in the reduction of that Hamiltonian, is given. These invariant combinations are obtained for a Hamiltonian containing up to eighth degree operators. The adaptation to the A and S forms of the Watson Hamiltonian and their utility in conversion of coefficients from one form to another is discussed.     

Erratum to: “Schwinger model in noncommutating space–time” [Phys. Lett. B 638 (2006) 292]

A calculational error was crept in the expression of the Hamiltonian (Eq. (14)) in original article. We give the correct form of the Hamiltonian and also the correct form of the subsequent equations which depend on the Hamiltonian. The corrections are all of numerical nature and do not affect the physical conclusions in any fundamental way.     

A Lie algebra structure on variation vector fields along curves in 2-dimensional space forms

A Lie algebra structure on variation vector fields along an immersed curve in a 2-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure for plane curve motions. The Hamiltonian form and the integrability of the planar filament equation are finally discussed from this point of view.     

正则变换与二粒子耦合体系哈密顿量的对角化技术

把耦合项为Ｃ（ａ＾１ａ２＾＋ａ２＾＋ａ１）＋Ｄ（ａ＾＋１ａ＋２＋ａ２ａ１）的Ｈａｍｉｌｔｏｎ量写成超矩阵相乘的形式，通过正则变换使其对角化。     

Hamilton系统的Mei对称性、Noether对称性和Lie对称性

研究Hamilton系统的形式不变性即Mei对称性，给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明本文结果的应用. 关键词： Hamilton系统 Mei对称性 Noether对称性 Lie对称性 守恒量