孤立波方程的保结构算法

讨论了孤立波方程的保结构差分算法,以一些经典的孤立波方程为例,如KdV,sine-Gordon,K-P方程,给出了它们的辛和多辛结构,说明辛和多辛算法的可适用性．提出局部守恒算法和广义保结构算法的概念,它们是保结构算法的概念自然推广．还给出一种能系统构造局部守恒格式的复合方法．数值例子说明,保结构数值能很好模拟各种孤立波的演化。     

量子系统保结构计算新进展

本文主要介绍量子系统保结构计算最新进展情况,分以下几部分内容:哈密顿系统的辛算法、适合于量子系统的哈密顿量显含时间的辛算法、A2B模型分子和双原子分子系统的经典轨迹辛算法计算、双原子分子CO在激光场中的经典轨迹的辛算法计算及其振动和解离、定态Schr dinger方程的辛形式及求解定态Schr dinger方程本征值问题的辛 打靶法、含时Schr dinger方程的保结构算法及其在激光原子物理中的应用、伪分立态模型、强激光与原子相互作用的渐近边界条件、"非齐线性正则方程"的辛算法及其在计算强激光场中一维原子的多光子电离和高次谐波发射中的应用以及Heisenberg方程的保结构计算等等。     

量子系统保结构计算新进展

本文主要介绍量子系统保结构计算最新进展情况,分以下几部分内容:哈密顿系统的辛算法、适合于量子系统的哈密顿量显含时间的辛算法、A2B模型分子和双原子分子系统的经典轨迹辛算法计算、双原子分子CO在激光场中的经典轨迹的辛算法计算及其振动和解离、定态Schr dinger方程的辛形式及求解定态Schr dinger方程本征值问题的辛 打靶法、含时Schr dinger方程的保结构算法及其在激光原子物理中的应用、伪分立态模型、强激光与原子相互作用的渐近边界条件、"非齐线性正则方程"的辛算法及其在计算强激光场中一维原子的多光子电离和高次谐波发射中的应用以及Heisenberg方程的保结构计算等等。     

变形谐振子势的能谱方程

讨论了3种变形谐振子势:左右两边不同参数的谐振子势、左边方形势加右边谐振子势和谐振子势中间加δ势中的能量本征态函数.这些函数都可以由厄米函数表示.由波函数及其一次导数在原点的衔接条件,得到了能谱方程.     

箱势中有吸引相互作用的中性原子体系的非性线薛定谔方程的严格解

给出了有吸引相互作用的中性原子体系的能级和波函数在一维箱势中的解析解和三维球方势中的数值解,分析了原子间的吸引作用对能级和波函数的影响,并与排斥相互作用情形的解进行了比较,讨论了吸引相互作用对玻色－爱因斯坦凝取的影响。     

紧束缚势和修正的嵌入原子势计算液态Sn双体相关函数差异

对500个Sn原子分别用两种模型（紧束缚势和修正的嵌入原子势）计算了400℃~1700℃温度范围内纯Sn的双体相关函数g（r）。将计算结果与实验数据进行了对比分析,发现两种计算结果都能基本上反映液态Sn的结构及其随温度的变化情况：原子最近邻距离与实验结果相近;随着温度降低,双体相关函数第一峰变得尖锐,第二峰变得明朗。修正的嵌入原子势模型得到的双体相关函数的第一峰右侧有个突起的肩膀,这在实验结果中也被发现,而紧束缚势模型得到的双体分布函数肩膀不明显。     

紧束缚势和修正的嵌入原子势计算液态Sn双体相关函数差异

对500个Sn原子分别用两种模型(紧束缚势和修正的嵌入原子势)计算了400℃～1700℃温度范围内纯Sn的双体相关函数g(r).将计算结果与实验数据进行了对比分析,发现两种计算结果都能基本上反映液态Sn的结构及其随温度的变化情况:原子最近邻距离与实验结果相近;随着温度降低,双体相关函数第一峰变得尖锐,第二峰变得明朗.修正的嵌入原子势模型得到的双体相关函数的第一峰右侧有个突起的肩膀,这在实验结果中也被发现,而紧束缚势模型得到的双体分布函数肩膀不明显.     

环形非球谐振子势Klein-Gordon方程的束缚态

用分离变量方法讨论了在环形非球谐振子标量势和矢量势相等条件下的Klein-Gordon方程的束缚态解.给出了用广义连带勒让得多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数，获得了精确的束缚态能谱方程. 关键词： 环形非球谐振子势 Klein-Gordon方程 束缚态     

Dirac方程的数值解法及其在原子总能量计算中的应用

中心势近似下径向Dirac方程的求解是相对论性原子(离子)结构计算的基础.本文通过相对论性方程中径向波函数大分量与非相对论方程径向波函数的类比,提出了径向Dirac方程的一种数值解法.为了验证数值解法的精度和可靠性,首先将数值结果与类氢势作用下的解析解进行比较.然后,将这种算法扩展到基于解析势的相对论性原子结构计算中,并将计算出的总能量与实验结果和其他方法得到的结果进行对比.     

μ原子的核结构效应

由于μ-子的轨道半径很小,利用它作为探针来研究核的结构具有一定的优势。本文以原子核按电荷均匀分布的球为例,对μ原子的能量作了计算和修正,结果与实验值符合较好。     

受迫振子的对称性与守恒量

讨论受迫振子体系的对称性和守恒量,导出了其含时位势的具体形式,给出了相应的对称变换算符,并讨论了线谐振子体系的含时守恒量.     

Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity

The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity isobtained by making a specific coordinate transformation and by using the method of time-dependent invariant.     

Coherent states of a damped harmonic oscillator

We construct here the coherent states (annihilation operator eigenstates) of a damped harmonic oscillator. These coherent states, which are normalizable, have the desired behaviour in the classical limit (ℏ→0).     

Even and Odd Coherent States for Time-Dependent Harmonic Oscillator

The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.     

Evolutions of Yang Phase Under Cyclic Condition and Adiabatic Condition

There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the evolutions of Yang phase under the cyclic condition and the adiabatic condition for the generaltime-dependent harmonic oscillator, thus reveals the intimate relations between these three non-integrable phases.     

Evolutions of Yang Phase Under Cyclic Condition and Adiabatic Condition

There are three non-integrable phases in literatures： Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the evolutions of Yang phase under the cyclic condition and the adiabatic condition for the general time-dependent harmonic oscillator, thus reveals the intimate relations between these three non-integrable phases.     

Even and Odd Coherent States for Time-Dependent Harmonic Oscillator

The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time-dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.     

Symmetries and conservation laws of the damped harmonic oscillator

We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.      

Piecewise optimal linearization method for nonlinear stochastic differential equations

A method for estimating the dynamical statistical properties of the solutions of nonlinear Langevin-type stochastic differential equations is presented. The non-linear equation is linearized within a small interval of the independent variable and statistical properties are expressed analytically within the interval. The linearization procedure is optimal in the sense of the Chebyshev inequality. Long-term behavior of the solution process is obtained by appropriately matching the approximate solutions at the boundaries between intervals. The method is applied to a model nonlinear equation for which the exact time-dependent moments can be obtained by numerical methods. The calculations demonstrate that the method represents a significant improvement over the method of statistical linearization in time regimes far from equilibrium.Supported in part by the National Science Foundation under Grants CHE77-16307 and PHY76-04761.