原子基态求法的探讨

在最外层电子分布中,d壳层出现了抢电子的现象,它造成原子基态求法的困难.同时应用一般方法求出少数原子基态与理论不符,有些教材对这几种原子基态提出3种不同看法.本文就这两种现象进行了分析和说明.     

The ground states and pseudospin textures of rotating two-component Bose–Einstein condensates trapped in harmonic plus quartic potential

The ground states of two-component miscible Bose–Einstein condensates(BECs) confined in a rotating annular trap are obtained by using the Thomas–Fermi(TF) approximation method.The ground state density distribution of the condensates experiences a transition from a disc shape to an annulus shape either when the angular frequency increases and the width and the center height of the trap are fixed,or when the width and the center height of the trap increase and the angular frequency is fixed.Meantime the numerical solutions of the ground states of the trapped two-component miscible BECs with the same condition are obtained by using imaginary-time propagation method.They are in good agreement with the solutions obtained by the TF approximation method.The ground states of the trapped two-component immiscible BECs are also given by using the imaginary-time propagation method.Furthermore,by introducing a normalized complex-valued spinor,three kinds of pseudospin textures of the BECs,i.e.,giant skyrmion,coaxial double-annulus skyrmion,and coaxial three-annulus skyrmion,are found.     

Reconstruction of dynamics from the vacuum in lattice theories

The Coester-Haag scheme to define the dynamics from the vacuum is applied to lattice theories. As an example the reconstruction algorithm is carried out for two trial ground states. The reconstruction approach may by itself define the theory or, when coupled with a variational calculation and a fixed external Hamiltonian, it provides a method to find the proximity of the trial ground states to actual states of the theory. This technique is applied to the reconstruction examples in the continuum limit.     

一种确定双原子分子基电子态的新方法

针对某些双原子分子基电子态与激发态势能曲线存在相交,从而引起利用从头计算确定分子基电子态时因初始输入不同而确定出的基态不同的情况,提出了一种将势能曲线计算和优化计算相结合确定基电子态的方法,并运用它确定B+2分子的基电子态.解释了文献中对于它的基电子态的计算出现不同结果的原因.     

Extension of the Local Approach to excited states of molecules

The Local Approach for the calculation of electronic correlation energies in molecules is generalized to excited states. Within the Local Approach correlated states are obtained by applying a local projection operator on the Hartree-Fock ground state or simple reference states, which are used as zeroth order approximations for the excited states, respectively. In the case of excited states one has in addition to require the correlated states to be orthogonal on the states lower in energy. This is done by using Schmidt's orthogonalization. The method is applied to a simple model of the H₆-ring for which an exact solution is available. The results obtained are of comparable quality as for the ground state.     

A new particle-hole approach to collective states

The relevance of the particle-hole space is demonstrated by showing that in some commonly used formalisms the first excited state lies entirely within the particle-hole space generated from the correlated ground state. This property is proved for several cases of angularmomentum projection — projected Hartree-Fock method (PHF) — and for the generator coordinate method in the Gaussian overlap approximation, while in other cases it has been verified only numerically. A new method is presented for the approximate calculation of energies and transition amplitudes of particle-hole excited states. Only hermitian one-body operators are used to generate the excited states. The two-body density matrix of a correlated state approximating the ground state is required as input data. The formula is tested on the 2⁺ and 3^? states of ⁸Be and ¹²C by using the PHF ground state. Where comparison is possible the method gives better agreement with PHF and experiment than the extended random-phase approximation.     

A continuation BSOR-Lanczos–Galerkin method for positive bound states of a multi-component Bose–Einstein condensate

We develop a continuation block successive over-relaxation (BSOR)-Lanczos–Galerkin method for the computation of positive bound states of time-independent, coupled Gross–Pitaevskii equations (CGPEs) which describe a multi-component Bose–Einstein condensate (BEC). A discretization of the CGPEs leads to a nonlinear algebraic eigenvalue problem (NAEP). The solution curve with respect to some parameter of the NAEP is then followed by the proposed method. For a single-component BEC, we prove that there exists a unique global minimizer (the ground state) which is represented by an ordinary differential equation with the initial value. For a multi-component BEC, we prove that m identical ground/bound states will bifurcate into m different ground/bound states at a finite repulsive inter-component scattering length. Numerical results show that various positive bound states of a two/three-component BEC are solved efficiently and reliably by the continuation BSOR-Lanczos–Galerkin method.     

On the stability of parameters of molecular models in the parametric method of the theory of vibronic spectra

We have studied the stability of the system of parameters used in the parametric method of the theory of vibronic spectra of polyatomic molecules with respect to whether the initial structural-dynamic model of the ground state of a molecule is formed either by the fragmentary method or by direct quantum-chemical calculation. Modeling of excited states and spectra of the stilbene-h ₁₂ and stilbene-d ₁₂ molecules showed that, although the initial models of the ground states are significantly different, calculated changes in the geometry that occur upon excitation and electronic-vibrational spectra of the models are close and quantitatively agree with experiment. This indicates that the parameters of the method are stable and are applicable for performing predictive calculations of vibronic spectra based on models of the ground states created by different methods. We show that the fragmentary method has a considerable advantage, since models created by this method take into account the continuity of the structure in series of related compounds and calculations can be easily performed for molecules of arbitrarily high complexity. We show that direct quantum-chemical calculations are important in the case of molecules with unknown structural-dynamic models of fragments in the ground states.     

磁场中量子点四电子系统的基态性质

利用少体物理的方法，研究了磁场中二维量子点四电子系统基态能量与角动量间的变化关系，以及磁场强度和约束势的大小对四电子系统基态的影响.数值计算表明，量子力学对称性是幻数角动量出现的重要因素. 关键词：     

用玻尔理论统-处理氢原子、电子偶素和氦原子基态能级

用玻尔氢原子理论处理氢原子和电子偶素基态的方法，在假定了氦原子基态的经典模型后，给出了氦原子基态能级和半径，并与实验和量子力学变分法计算的结果作比较，说明玻尔氢原子理论对氦原子基态能级的计算有一定的意义．     

用SAC-CI方法研究Si(CH3)2O双自由基的基态、激发态、阳离子态和阴离子态

采用Nakatsuji提出的对称匹配耦合簇相互作用(SAC-CI)方法,计算了Si(CH3)2O双自由基分子的基态,单重三重激发态,阳离子二重态和阴离子二重态的激发能,光电子谱,电离能等.结果表明,SAC-CI方法比TDDFT有明显优势.     

The Analytical Wavefunctions of SU(3) Limit in the Interacting Boson Model

A projection method to calculate the physical states from intrinsic states is put forward. Using this projection method, the physical states of the ground state band in the interacting boson model (IBM) SU(3) limit are calculated. The wave functions are expressed in terms of the building blocks of the IBM wave functions.     

Analytic Solution of Strongly Coupling SchrödingerEquations

A recently developed expansion method for analytically solving the ground states of strongly coupling Schrödinger equations by Friedberg, Lee, and Zhao is extended to excited states and applied to power-law central forces for which scaling properties are proposed. As examples for application of the extended method, the Hydrogen atom problem is resolved and the low-lying states of Yukawa potential are approximately obtained.     

Classical probability density distributions with uncertainty relations for ground states of simple non-relativistic quantum-mechanical systems

The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown that classical distributions are remarkably improved by incorporating into them the Heisenberg uncertainty relation between position and momentum. Even the crude form of this incorporation makes the agreement between classical and quantum distributions unexpectedly good, except for the small area, where classical momenta are large. It is demonstrated that the slight improvement of this form makes the classical distribution very similar to the quantum one in the whole space. The obtained results are much better than those from the WKB method. The paper is devoted to ground states, but the method applies to excited states too.     

Delta-Davidson method for interior eigenproblem in many-spin systems

Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,little attention has been paid to the central states,which are exponentially close to each other in terms of system size.We propose a delta-Davidson(DELDAV)method to efficiently find such interior(including the central)states in many-spin systems.The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem.Numerical experiments on Ising spin chain and spin glass shards show the correctness,efficiency,and robustness of the proposed method in finding the interior states as well as the ground states.The sought interior states may be employed to identify many-body localization phase,quantum chaos,and extremely long-time dynamical structure.     

The single-determinant approximation with a local potential for excited states

The specific features of the calculations of the electronic structure in the approximation of a local exchange potential that is identical for all the electrons involved are considered. An optimized effective potential method is proposed for calculating the energies of excited electronic states of the same symmetry. A single-particle Schrö dinger equation is derived for an excited state whose orbitals are described by a single-determinant wave function orthogonal to the ground state. The equations determining the local potential for excited states are obtained within the variational approach. The solution to these equations is analyzed in the framework of the parameterized representation of the effective potential. The efficiency of the proposed method is demonstrated by calculating the energies of three excited states of the same symmetry for a HeH molecule. The difference between the results obtained by the Hartree-Fock method and the method proposed in this paper is equal, on average, to 0.05%. A comparison with the results obtained from precise calculations based on the configuration interaction method shows that the accuracy in determining the energy of the excited states by the optimized effective potential method is comparable to the accuracy in calculating the energy of the ground state.     

氦原子低激发态能量的变分计算

给出了一种用变分法计算氦原子低激发态（电子组态为1s2s,1s2p)能量的具体方法,计算过程中解决了激发态波函数与基态波函数的正交性,计算结果与实验值与相当接近。     

关于量子基态的一种解法

通过一个积分变换,量子系统的能量本征值问题可转化为求解非线性的Riccati方程,由它可以容易地求出基态能量及相应的波函数,讨论了此方法与通常的因子化方法的关系并以各种常见的系统作为显示此方法优越性的示范。 关键词：     

On the potential energy curves of LaO molecule

Turning points for several electronic states of LaO molecule are calculated using the Rapid method by Morse function, and compared with those obtained by RKR method. The electronegativity potential function and RKR potential functions are compared for the ground state of the molecule and an estimate of dissociation energy of LaO molecule in the ground state is reported.     

Universality of striped morphologies

We present a method for predicting the low-temperature behavior of spherical and Ising spin models with isotropic potentials. For the spherical model the characteristic length scales of the ground states are exactly determined but the morphology is shown to be degenerate with checkerboard patterns, stripes and more complex morphologies having identical energy. For the Ising models we show that the discretization breaks the degeneracy causing striped morphologies to be energetically favored and therefore they arise universally as ground states to potentials whose Hankel transforms have nontrivial minima.