一维无限深势阱内粒子的动量概率分布

本文对现行教材中一维无限深势阱内粒子概率分布的两种不同结论进行了较深入的讨论。认为ｖｏｎ Ｎｅｕｍａｎｎ公理系统在处理无限深势阱问题时确有困难，最后采用一种新的态空间概念，使上述困难得以解决。     

无限深方势阱本征值和本征态的三种求解方法

一维无限深方势阱模型是量子力学理想模型,经典教材中势阱的边界一般取得比较特殊.或关于坐标原点具有对称性,或势阱左边界位于坐标原点.本文首先展示了如何利用3种方法求解一维任意边界无限深方势阱能量本征值和对应的本征态,不同方法得到的结果彼此之间等价,讨论分析了这3种方法的推导结果,然后得到关于一维任意边界无限深方势阱能量本征值和本征态的通式,从中比较容易看出这两个物理量均与阱宽有关,并且本征波函数与边界值有关,最后将一维结果拓展到二维和三维任意边界无限深方势阱情况.     

关于无限深势阱内粒子动量概率分布的讨论

关于无限深势阱内粒子动量概率分布的讨论关于一维无限深势阶中粒子动量概率分布的问题，自本刊在１９８３年第６期发表了曾锡滨同志的文章以来，不时有人投稿，对朗道与泡利的两种不同处理方法进行讨论。现在我们发表云南姜存志同志和山东倪宏慈同志的来稿，并附以一篇“...     

类经典态——谐振子和无限深方势阱

把坐标平均值随时间的变化和在宏观条件下与经典解相同的量子态定义为类经典态,并求解了一维谐振子和无限深方势阱的类经典态,有助于从波动力学角度理解量子到经典过度的问题. 关键词： 量子经典对应 类经典态 谐振子 无限深方势阱     

无限深势阱中粒子动量概率分布的数值分析

一维无限深势阱中本征态粒子的动量呈现负无穷到正无穷且有无数个节点的对称连续分布.本征态粒子的无量纲动量概率密度分布一般由两个主峰和无数的次峰组成,经典动量和最概然动量都分布在主峰区域内.数值计算结果表明动量谱在两个主峰区域内的概率极限值约为0.902 8,测量所包含的次峰数量越多则粒子出现的概率越接近1.粒子经典动量分布是量子动量分布在高测量精度和大量子数条件下的极限.     

量子力学中无限深势阱问题的教学研究

在一维问题的基础上探讨了二维无限深势阱的问题,发掘二维无限深势阱在不同边界约束情况下不同于一维问题的特征和应用.     

自由粒子在μ空间的运动描述

对一维自由粒子在μ空间的运动,经典力学和量子力学各自提供了看似不同、实则等价的两种描述.一些经典教材对这个问题的表述有误或者不完整.本文首先通过分析经典力学中自由粒子在一维盒子中和在全空间的运动,画出了μ空间的轨迹;然后通过分析量子力学中自由粒子在无限深势阱中和在全空间周期性边界条件下的运动,画出μ空间每个量子态占据的面积元.最后本文讨论了周期性边界条件下动量为零的态存在性,一个量子态在相空间中的体积元和不确定性关系之间的区别等问题.     

一维无限深势阱的扩展探讨

建立了势阱宽度变化的一维无限深势阱的动态模型,通过求解含时间的薛定谔方程,证明粒子通常处于叠加态,得出了系统能量处于不同值的概率,而这一概率可以理解为无辐射跃迁的概率.     

也谈量子力学的基础

本文通过在不同边界条件下动量算符的厄密性和自伴性的区分,给出了对量子力学的一维无限深方势阱中基态粒子的动量分布问题的严格分析,论证了量子力学基本假设的严谨性和自洽性.     

关于同一问题的两种不同解法

在一维无限深势阱中，运动粒子的动量概率分布函数。朗道与泡利所得结论不同这是量子力学者常感困惑并引起争论的一个问题，本文分析了结论不同的根源，并论述了当ｎ很大时，两个结论是趋于一致的。     

Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute values exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical approaches to these exponents so far can be divided into two groups, macroscopically oriented approaches, using kinetic theory or hydrodynamics, and more microscopically oriented random-matrix approaches in quasi-one-dimensional systems. In this paper, I present an approach using random matrices and weak-disorder expansion in an arbitrary number of dimensions. Correlations between subsequent collisions of a particle are taken into account. It is shown that the results are identical to those of a previous approach based on an extended Enskog equation. I conclude that each approach has its merits, and provides different insights into the approximations made, which include the Stoßzahlansatz, the continuum limit, and the long wavelength approximation. The comparison also gives insight into possible connections between Lyapunov exponents and fluctuations.     

Quantum theory of sticking: equivalence of various approaches and application to a simple model

The basic formulae of four different quantum mechanical approaches to the calculation of the sticking coefficient of an atom on a cold solid are re-examined in order to discuss the connections between them. All approaches pursued exactly give the same result, and this is exhibited for a one-dimensional model which is exactly solvable to provide closed-form formulae for the sticking coefficient. Numerical results, which reproduce the qualitative behaviour of atomic sticking, are presented for different assumed densities of substrate excitations responsible for the energy loss, including the physically important cases of low-energy single phonons, and low-energy electron-hole pairs in a metal.     

对Z0三喷注事例中色联接敏感可观测量的研究

将末态部分子的色分离联接引入JETSET事例产生器,通过用喷注的DURHAM判据y_cut及用喷注夹角限制事例形状,对Z⁰衰变进行三喷注事例挑选,发现可以得到对色联接敏感的三喷注事例.对于这类事例,末态强子的平均带电多重数及胶子喷注中的一系列可观测量对色联接的敏感性随y_cut值的减小而增大;在小y_cut值时,色中性流和色分离两种联接导致了显著差别.使通过实验测量鉴别部分子的色联接成为可能.     

Sensitive Observables for Color Connections in Three-Jet Events at Z0 Pole

By substituting the color separate singlet connections for the color neutral flow connections into JETSET7.4, we select the three-jet events according to DURHAM algorithm in e⁺e^－ annihilation at Z⁰ pole. We find that the ratio of the special three-jet events defined by constraining the angles between different jets is sensitive to different kinds of color connections. For these special events, different connections lead to significant differences for the charged particle multiplicity of events and properties of the gluon jet. The differences become larger as y_cut getting smaller. By taking appropriate y_cut, as 0.0005 in this paper, the differences between these two kinds of color connections should be discriminated by experiments.     

Density functionals and model Hamiltonians: Pillars of many-particle physics

Density-functional theory (DFT) and model Hamiltonians are conceptually distinct approaches to the many-particle problem, which can be developed and applied independently. In practice, however, there are multiple connections between the two. This review focuses on these connections. After some background and introductory material on DFT and on model Hamiltonians, we describe four distinct, but complementary, connections between the two approaches: (i) the use of DFT as input for model Hamiltonians, in order to calculate model parameters such as the Hubbard U and the Heisenberg J. (ii) The use of model Hamiltonians as input for DFT, as in the LDA + U functional. (iii) The use of model Hamiltonians as theoretical laboratories to study aspects of DFT. (iv) The use of special formulations of DFT as computational tools for studying spatially inhomogeneous model Hamiltonians. We mostly focus on this fourth combination, model DFT, and illustrate it for the Hubbard model and the Heisenberg model. Other models that have been treated with DFT, such as the PPP model, the Gaudin–Yang δ$\delta$-gas model, the XXZ chain, variations of the Anderson and Kondo models and Hooke’s atom are also briefly considered. Representative applications of model DFT to electrons in crystal lattices, atoms in optical lattices, entanglement measures, dynamics and transport are described.     

Synchronization in Complex Networks with Multiple Connections

In this paper a class of networks with multiple connections are discussed. The multiple connections include two different types of links between nodes in complex networks. For this new model, we give a simple generating procedure. Furthermore, we investigate dynamical synchronization behavior in a delayed two-layer network, giving corresponding theoretical analysis and numerical examples.     

Study of Colour Connections via Two-Jet Like Events in e+e－ Annihilation

We study the different properties of the two jet like events in e⁺e^－→Z⁰→hadrons under different color connections with the aid of the event generator JETSET. We find that the two kinds of colour connections at the interface of perturbative and nonperturbative QCD, i.e., colour neutral flow and colour separate singlet, lead to significant differences for some observables in the final states. Therefore, the measurements of these observables can be used to distinguish these two kinds of colour connections.     

Cohomological gravity

We construct a theory of cohomological gravity in arbitrary dimensions based upon a local vector supersyrnmetry algebra. The observables in this theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach different moduli spaces are obtained by introducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occurring differential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum field theory, and the discrete Regge calculus.This essay received an honorable mention from the Gravity Research Foundation, 1992-Ed.     

The algebraic structure of cohomological field theory

The algebraic foundation of cohomological field theory is presented. It is shown that these theories are based upon realizations of an algebra which contains operators for both BRST and vector supersymmetry. Through a localization of this algebra, we construct a theory of cohomological gravity in arbitrary dimensions. The observables in the theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach, different moduli spaces are obtained by introducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occuring differential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum field theory, and the discrete Regge calculus.     

On unique predictions for single spin azimuthal asymmetry

Theoretically there are two approaches to predict single spin azimuthal asymmetries. One is to take transverse momenta of the partons into account by using transverse momentum dependent parton distributions, while another is to take asymmetries as twist-3 effects. The non-perturbative effects in these approaches are parameterized with different matrix elements, and predictions can be different. Recently, gauge invariant definitions of transverse momentum dependent parton distributions were derived. With these definitions it can be shown that there are relations between non-perturbative matrix elements in these two approaches. These relations may enable us to unify two approaches and to have unique predictions for single spin azimuthal asymmetries. In this letter we derive these relations by using time-reversal symmetry and show that even with these relations the single spin azimuthal asymmetry in a Drell-Yan process is predicted differently in different approaches.Received: 2 July 2004, Published online: 24 September 2004