库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.     

晶体场理论引论(四)

晶体场中能级分裂的计算--行列式波函数方法(4-1)用微扰法计算晶体场中能级分裂的示例 用简并微扰法计算晶体场中自由离子能级的分裂时,晶体场哈密顿量作为微扰,自由离子波函数为基,求出矩阵元,解久期方程,求出一级能量修正值即晶体场中能级的分裂,同时可求出自由离子基函数的线性组合作为零级近似波函数.下面以3d1组态的能级为例.     

双电子二维量子点基态能量的计算

分别利用微扰法、精确的对角化方法和变分法计算了双电子二维量子点的基态能量,与早期无约束的哈特利-福克研究结果比较,发现三参量的变分波函数是基态的极好表征.     

双电子平面量子点基态能量的计算

由于库仑作用,目前的研究还得不到双电子平面量子点基态波函数和基态能量的精确解析解.分别利用微扰法、精确对角化方法和变分法,计算双电子平面量子点的基态能量,与早期的无约束哈特利-福克研究结果比较,发现三参量的变分波函数是基态的极好表征.且能对多电子平面量子点的基态描述提供参考.     

硼原(离)子内壳激发高自旋态能级和辐射跃迁

采用Rayleigh-Ritz变分方法计算了B原子(离子)内壳层激发高自旋态(~(4,5,6)L,L=S,P)里德伯系列的能量和精细结构劈裂,利用截断变分方法改进非相对论能量,并利用一阶微扰理论计算了相对论能量修正和质量极化效应修正,利用屏蔽的类氢公式计算了量子电动力学效应和高阶相对论效应,从而得到了高精度的组态能量.利用精确计算的波函数,计算了这些高自旋态的电偶极辐射跃迁波长、振子强度和辐射跃迁概率.通过长度规范和速度规范计算的振子强度的一致性证明了本文计算的波函数是精确的.相比其他理论计算结果,本文计算的高自旋态的能级及跃迁波长数据与实验数据符合得更好.对于一些高位的内壳层激发高自旋态,相关的能级和跃迁数据为首次报道,本文的计算结果对相关实验光谱谱线标定具有重要意义.     

参数微扰法计算氦原子基态能量

根据参数微扰法理论,选择有效核电荷数为z*=2-σ的两个类氢原子的ns态的波函数的组合,作为氦原子基态的1级至4级近似波函数.应用参数微扰法计算了氦原子基态4级近似能量.计算结果表明参数微扰法得到的氦原子基态4级近似能量与实验值的误差为ΔE=0.004922028e_s~2/a_0.     

重夸克偶素质量谱的相对论夸克模型研究（已撤稿）

使用量子场论中准势途径的相对论夸克模型,计算了重夸克偶素的质量谱.所采用的同味正反夸克间的有效相互作用包括通常的直接单胶子交换、单胶子湮没及具有相对论修正的标量和矢量线性禁闭的混合.得到了与实验上肯定的数据符合较好的拟合计算结果，并讨论了湮没项和相对论修正各项对能谱超精细分裂的作用. 关键词： 重夸克偶素 质量谱 相对论修正 湮没势     

类硼S离子K壳层激发共振态的辐射和俄歇跃迁

采用多组态鞍点变分方法计算了类硼S离子K壳层激发共振态1s2s~22p~2, 1s2s2p~3, 1s2p~(4 2,4)L(L=S, P,D)的非相对论能量和波函数,利用截断变分方法饱和波函数空间,改进体系的非相对论能量.利用微扰理论计算了相对论修正和质量极化效应,利用屏蔽的类氢公式计算了QED (quantum electrodynamics)效应和高阶相对论修正.进一步,考虑闭通道和开通道相互作用,计算了由俄歇共振效应引起的能级移动,从而得到了共振态的精确相对论能级.利用优化的波函数,计算了类硼S离子K壳层激发共振态的电偶极辐射跃迁的线强度、振子强度、跃迁率和跃迁波长.计算的振子强度和辐射跃迁率均给出了长度规范、速度规范、加速度规范的结果.三种规范结果的一致性表明了本文计算的波函数是足够精确的.利用鞍点复数转动方法计算了类硼S离子K壳层激发共振态的俄歇跃迁率、俄歇分支率和俄歇电子能量.本文的计算结果与其他文献数据符合较好.     

粲夸克辐射的死区效应

基于轻夸克辐射能量谱, 考虑夸克质量对部分子辐射能量损失的影响, 利用死区因子把轻部分子辐射能量损失谱推广到重部分子辐射能量损失的情形. 研究结果表明, 利用与夸克质量相关的死区因子推广轻夸克辐射能量损失谱得到的重夸克辐射能量损失谱, 与直接利用微扰QCD计算所得到的Djordjevic-Gyulassy(D-G)谱的结果一致, 且极大简化了重夸克辐射能量损失的计算.     

互补变分原理及其在微扰理论近似中的应用

以正则变分和线性变分函数为基础，对互补变分原理作了论证，推导出二阶能量修正的上界和不受任何条件限制的下界，对具体计算方法作了详细的研究，得出互补变分原理在微扰理论近似中的应用，所求氢原子和极化率结果比一般的发法的微扰法所得结果更接近于实验值，并指出这理论可以推广应用到激发态或处理高阶修正问题。     

Variational-integral perturbation corrections of some lower excited states for hydrogen atoms in magnetic fields

A variational-integral perturbation method(VIPM) is established by combining the variational perturbation with the integral perturbation.The first-order corrected wave functions are constructed,and the second-order energy corrections for the ground state and several lower excited states are calculated by applying the VIPM to the hydrogen atom in a strong uniform magnetic field.Our calculations demonstrated that the energy calculated by the VIPM only shows a negative value,which indicates that the VIPM method is more accurate than the other methods.Our study indicated that the VIPM can not only increase the accuracy of the results but also keep the convergence of the wave functions.     

一类非线性演化方程的新多级准确解

在Lamé方程和新的Lamé函数的基础上，应用小扰动方法和Jacobi椭圆函数展开法求解一类非线性演化方程（如mKdV方程，非线性Klein-Gordon方程Ⅱ等），获得多种新的多级准确解 .这些多级准确解对应着不同形式的周期波解.这些解在极限条件下可以退化为多种形式的孤 立波解，如带状孤立子、钟形孤立子等. 关键词： Jacobi椭圆函数 Lam函数 多级准确解 非线性演化方程 扰动方法     

Two-site two-electron generalized Hubbard-Holstein model: a perturbation study

The two-site two-electron generalized Hubbard-Holstein model is studied within a perturbation method based on a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation. The ground-state wave function and the energy are found including up to the seventh and eighth order of perturbation, respectively. The convergence of the perturbation corrections to the ground state energy, as well as to the correlation functions, are investigated. The kinetic energy and the correlation functions involving charge and lattice deformations are studied as a function of electron-phonon(e-ph) coupling and electron-electron interactions for different values of the adiabaticity parameter. The simultaneous effect of the e-ph coupling and Coulomb repulsion on the kinetic energy shows interesting features.     

非线性薛定谔方程的新多级包络周期解

基于Lamé方程和新的Lamé函数,应用摄动方法和Jacobi椭圆函数展开法求解了非线性薛定谔方程,获得多种新的多级准确解。这些解对应着不同的形式的包络周期解。这些解在极限条件下可以退化为各种形式的包络孤波解。     

Lam函数和非线性演化方程的多级准确解的不变性

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.并在Lam方程和Lam函数的基础上，应用 Jacobi椭圆函数展开法求出了非线性演化方程的多级准确解，从而得到了多级准确解中存在的守恒形式. 关键词： Lam函数 Jacobi椭圆函数 多级准确解 非线性演化方程 扰动方法 不变性     

Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函 数展开法求得了零级近似方程的准确解，并由此得到一级近似方程和二级近似方程分别满足 齐次Lam方程和非齐次Lam方程，应用Lam函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样，就求得了非线性演化方程的多级准确解. 关键词： Jacobi椭圆函数 Lam函数 多级准确解 非线性演化方程 扰动方法     

Correlation corrections based on the Schrödinger equation with a local potential

A compromise version of calculation of the ground state electronic energy is proposed that combines both the density functional theory and the wave function formalism. Single-particle orbitals and energies are determined by solving the Kohn-Sham equations with a local effective potential, which depends on the parameters determined by the variational principle. Correlation corrections are calculated using the Rayleigh-Schrödinger perturbation theory in the zero-order approximation of the Möller-Plesset theory. The specific features of the expressions for the corrections to the wave function and the energy determined in terms of the Kohn-Sham orbitals are considered. This approach, in contrast to the well-known optimized effective potential method, can be applied with equal computational expenditures to both atoms and molecules. A comparative analysis for 20 helium-like atoms showed that the scheme proposed provides better agreement with the “exact” values of the energy in the second order of the perturbation theory in comparison with the results obtained using the conventional exchange-correlation potentials BLYP and PW91. A similar trend is also observed for diatomic hydrides (from LiH to FH), although, in contrast to the atoms, the deviations from the experimental estimates of the energy are less systematic.     

势阱中粒子能级与波函数微扰计算的代数递推公式

利用超位力定理（HVT）和Hellmann-Feynman定理（HFT）,导出了由有精确解的势阱的能级值用微扰法直接计算一维势阱的各级近似能级的普遍代数公式,并导出由能级近似值计算定态波函数近似表达式的代数公式,给出了代数公式具体应用的几个典型一维势阱实例,此法可推广到二维势阱与三维势阱的情形。     

Electrons in a strong magnetic field on a disk

The problem of interacting electrons moving under the influence of a strong magnetic field in two dimensions on a finite disk is reconsidered. First, the results of exact diagonalizations for up to N = 9 electrons for Coulomb as well as for a short-range interaction are used in the search for a peculiar ground state corresponding to filling factor 1/3. Not for the Coulomb, but only for the short-range interaction, can the 1/3-state be safely identified amongst the spectra of various filling factors close to 1/3. Second, the propositions of the concept of quasiparticles, as used in the hierarchical theory, are examined in view of the exact results for the disk geometry. Whereas the theory for the quasiholes is in complete accordance with the spectra, for the quasielectrons, finite size corrections make an analysis difficult. For the quasielectron energy, an extrapolation to N→ ∞ is given and compared with the corresponding extrapolations of three different proposals for trial wave functions. While the limiting value for the best trial wave function is very close to the limit of the exact results, the behavior of the finite size corrections of the exact energies and of the trial wave functions, respectively, is qualitatively rather different.     

Relativistically corrected masses of ground-state baryons in hyperspherical harmonic quark model

The masses of the ground-state light baryons are calculated in the quark model. The unperturbed wave functions correspond to a hyperspherical harmonic confinement. The perturbation includes a short-range potential and all the relevant relativistic corrections of the order ofv ²/c ². Results are compared with the experimental values and found to be in good agreement. This may be a test not of the hyperspherical harmonic model so much as of the feasibility of a simple (but consistent) relativistically corrected fit of the light baryon masses.