参数微扰法中基态能量与近似级数的关系

基于参数微扰法并使用满足空间交换对称性的波函数计算了氦原子的2到12级近似基态能量.计算表明,随着近似级数的增加,氦原子基态能量逐渐降低,改变量越来越小,基态能量与实验值的绝对误差存在一定起落.因此,选择合适的近似级数对氦原子基态能量的精确计算具有重要作用.     

Theory of pairing symmetry in the vortex states

We investigate pairing symmetry in an Abrikosov vortex and vortex lattice. It is shown that the Cooper pair wave function at the center of an Abrikosov vortex with vorticity m has a different parity with respect to frequency from that in the bulk if m is an odd number, while it has the same parity if m is an even number. As a result, in a conventional vortex with m = 1, the local density of states at the Fermi energy has a maximum (minimum) at the center of the vortex core in an even (odd)-frequency superconductor. In the vortex lattice of s-wave superconductor, we find that only odd-frequency pairing is present at the core centers, while at the midpoint of the vortex lines, only even-frequency pairing exists. Thus, the odd and even-frequency pairings also form the lattice in the vortex lattice state. We also propose a scanning tunneling microscope experiment using a superconducting tip to explore odd-frequency superconductivity.     

Classical ground states in one dimension

We give conditions on an interaction sufficient to guarantee that in one dimension it yield a periodic ground state with one or two particles per unit cell.Research supported in part by NSF Grant MCS 81-01596-A01.     

The infinite-volume ground state of the Lennard-Jones potential

We consider a finite chain of particles in one dimension, interacting through the Lennard-Jones potential. We prove the ground state is unique, and approaches uniform spacing in the infinite-particle limit.Research supported in part by NSF grant MCS 78-01520.     

Broken symmetry in antiferromagnets

We discuss limitations of the conventional ‘broken symmetry’ picture of the Heisenberg antiferromagnet. The exact results on the ground state of the linear chain and of the three-dimensional Hamiltonian do not show a ‘degeneracy of the vacuum’. With the help of a solvable model it is shown that the correlations in the ground state may have the Néel character, as revealed by the neutron experiments, even though the ground state is quite different from the Néel states. There is no Goldstone mode in the linear chain. The spin of the antiferromagnetic spin wave is 1/2. But the physical states have a doublet of the spin waves which could be regarded as degenerate states of spin 1 and spin 0. The fermionic character is suppressed and the bosonic character revealed, as in the decolouring phenomena in quantum field theory. It is plausible that in the three-dimensional case also there is no Goldstone mode.     

A conformai,symmetry broken model for gravity

Starting from Padmanabhan's fully conformally invariant action, we obtain gravity as a spontaneously broken theory. Newton's constant and the cosmological constant follow from the breakdown of the conformal symmetry at the tree approximation. For small oscillation of the scalar field about the fundamental state, the matter field degenerates into two decoupled fields.     

Influence of different fields of mesons on the pseudospin symmetry in single-neutron resonant states

In the framework of the relativistic mean field theory combined with the complex momentum representation method, we elucidate the pseudospin symmetry in the single-neutron resonant states and its dependence on the \begin{document}$\sigma$\end{document}, \begin{document}$\omega$\end{document}, and \begin{document}$\rho$\end{document} meson fields. Compared with the effect of the \begin{document}$\rho$\end{document} field, the \begin{document}$\sigma$\end{document} and \begin{document}$\omega$\end{document} fields provide the main contributions to the pseudospin energy and width splitting of the resonant pseudospin doublets. Especially, we compare quantitatively the pseudospin wave functions' splittings in resonant doublets, and investigate their dependencies on different fields of mesons, which is consistent with that of energy and width splittings. Current research is helpful to understand the mechanism and properties of pseudospin symmetry for resonant states.     

The ground state for sticky disks

It is proven that the ground state of the two-dimensional sticky potential is the triangular lattice.Research supported in part by NSF grant MCS 78-01520-A01.     

Crystallinity in two dimensions: A note on a paper of C. Radin

To demonstrate the crystallinity of the soft disk ground state, a modified treatment of this model is given, as Radin's proof of a crucial lemma can be shown to be incorrect.     

相对论情况下赝自旋对称性势场中运动粒子的束缚态

在赝自旋对称性条件下,分别求解了在M rse型和Tan2(πηr)型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.     

在赝自旋对称性势场中运动的相对论粒子的束缚态

在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.     

The ground state for soft disks

We consider some two-dimensional models of point particles interacting through short-range two-body potentials and prove that their zero temperature, zero pressure states are crystalline.Research supported in part by NSF grant No. 78-01520-A01.     

The breaking of intrinsic reflection symmetry in nuclear ground states

Negative-parity excited states of doubly even nuclei have earlier been attributed to vibrational excitations. This paper shows that an interpretation starting from a reflection asymmetric intrinsic state is more appropriate for certain nuclei in the radium region. Theoretical evidence for stable octupole deformation comes from a deformed shell-model calculation in which we use a single-particle potential with a realistic radial shape and a finite-range interaction for the surface energy. The octupole effect systematically improves the agreement between theoretical and experimental masses. The low-lying O⁺ excitations observed in experiment are compatible with the calculated collective octupole potentials. The possibility of obtaining further evidence from the spectroscopy of odd-mass nuclei is considered in an exactly solvable model, which shows that the smaller energy splitting observed in odd-A parity doublets mainly reflects single-particle fragmentation of the collective mode. The systematics of theoretical shell structure and experimental spectroscopy suggests the presence of other regions of octupole collectivity near the limits of stability.     

类氦原子体系基态能量的变分法数值研究

选取由指数形式函数的线性组合所构成的试探波函数,利用变分法对类氦原子体系的基态能量进行了数值计算,计算中利用拟牛顿法求非线性方程组的一组实根,计算结果与实验值相当接近．计算表明：当n由1增大到2时,能量的计算值有较大的改进,但由于选取的变分波函数没有考虑到电子关联作用,所以计算只能达到一定的精确度．     

Emden方程的Mei对称性、Lie对称性和Noether对称性

研究Emden动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Emden方程的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，给出一个例子说明结果的应用. 关键词： Emden动力学方程 Mei对称性 Noether对称性 Lie对称性     

氩原子基态波函数和能量的解析计算

以第一性原理和变分原理为基础,给出了氩原子基态波函数的一种解析表达式,计算了基态氩原子(含类氩离子)的能量,导出了所涉及的所有积分的解析表达式.对氩原子,所得到的能量理论值与实验值的相对误差为0.22%.     

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