变形对称双阱势

利用变形双曲函数,将对称双阱势推广为变形对称双阱势模型.证明了该势模型是五参量指数型势模型的特例.运用超对称WKB近似和五参量指数型势模型的能谱公式,获得了变形对称双阱势模型的能谱公式.     

Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

We show that the 1-dimensional Schrödinger equation with a quasiperiodic potential which is analytic on its hull admits a Floquet representation for almost every energyE in the upper part of the spectrum. We prove that the upper part of the spectrum is purely absolutely continuous and that, for a generic potential, it is a Cantor set. We also show that for a small potential these results extend to the whole spectrum.     

Discrete and continuum models for calculating the phonon spectra of carbon nanotubes

The vibration spectrum of perfect carbon nanotubes is studied using a two-parametric potential which includes pairwise and three-particle interatomic interactions. This potential was proposed by Keating and allows one to take into account the elasticity of pairwise interatomic bonds and the elasticity associated with a change in the angle between directional interatomic bonds in covalent crystals. Using the Keating potential, the vibration spectrum of a graphite monolayer is calculated and fitted to the vibration spectrum of crystalline graphite, thereby determining the parameters of the potential. With these parameters, the phonon spectra of perfect monolayer graphite nanotubes are calculated. A continuum model, in which a monolayer nanotube is represented as an elastic cylindrical shell of a finite thickness, is also discussed. Within this model, the vibration spectrum of a nanotube is calculated numerically in the long-wavelength limit as a function of the radius and thickness of the nanotube.     

Structure in the aluminum 1s soft x-ray appearance potential spectrum

The Al 1s level soft X-ray appearance potential spectrum for clean and oxidized Al has been observed. In the spectrum of the clean metal, structure related to an edge singularity and a plasmon satellite is distinguished. The plasmon coupling strength in the appearance potential spectrum is found to be almost equal to that in X-ray photoelectron spectroscopy and bremsstrahlung isochromat spectroscopy.     

Physical aspects of the shape of electron emission spectra for ferroelectric electrets

A correlation between the specific features of the electron emission spectrum of a ferroelectric electret and the behavior of the potential at the surface of the sample is determined within the theoretical approach proposed. The physical nature of the main features in experimental emission spectra is interpreted in terms of the behavior of the potential relief. It is revealed that the electret charge relaxation affects the spectrum shape due to the bifurcation (branching) of singularities in the spectrum.     

一维幂次势阱中粒子能谱规律的分析

分析了一维幂次势阱中粒子的能谱,讨论了能谱形状随幂次变化的规律．     

Murrell-Sorbie势能参数与双原子分子光谱数据的关系研究

研究了Murrell-Sorbie势能参数与双原子分子光谱数据的关系.根据光谱数据编程计算了卤化氢分子的力常数和Murrell-Sorbie势能参数.反过来,运用ab initio和非线性最小二乘法拟合出了HF分子的Murrell-Sorbie势能函数和势能参数;并由此计算了HF分子的光谱数据,与实验光谱数据符合较好.这对难以获得实验光谱数据的双原子分子和离子的动力学研究有一定的参考价值.     

强激光场中氢负离子双光子电离能量谱的研究

利用强场近似(Strong field approximation,SFA)方法研究氢负离子(H-)在强激光场中双光子电离的能量谱,所得到的电离谱随角度的变化规律与实验结果符合得很好.进一步的研究表明,H-离子在强激光场中双光子电离的能量谱与有质动力能有关.激光场强度越大,光电子的有质动力能也越大,能量谱向左移动越明显...     

Electronic spectrum and ballistic transport in a helical nanotube

A model of a helical nanotube permitting analytical calculation of the spectrum and wave functions is proposed and studied. It is shown that the specific character of the symmetry of the Hamiltonian results in an electronic spectrum having no band structure despite the periodicity of the potential along the system axis. A two-dimensional ribbon rolled into a helix and a quasi-one-dimensional helix in a magnetic field are considered as limiting cases of the model. It is shown that the presence of additional local minima in the subbands of the electronic spectrum leads to a nonmonotonic dependence of the ballistic conductance of the system on the chemical potential.     

幂次中心势阱中粒子能谱规律的分析

分析了幂次中心势阱中粒子的能谱，讨论了粒子能谱形状随幂次变化的规律     

强激光场中氢负离子双光子电离能量谱的研究

利用强场近似（Strong field approximation,SFA）方法研究氢负离子（H ）在强激光场中双光子电离的能量谱,所得到的电离谱随角度的变化规律与实验结果符合得很好.进一步的研究表明, H 离子在强激光场中双光子电离的能量谱与有质动力能有关.激光场强度越大,光电子的有质动力能也越大,能量谱向左移动越明显.我们的结果表明,使用强场近似是一种研究负离子在强激光场中电离过程的有效方法.     

Spectral Analysis of the Disordered Stochastic¶1-D Ising Model

We consider the generator of the Glauber dynamics for a 1-D Ising model with random bounded potential at any temperature. We prove that for any realization of the potential the spectrum of the generator is the union of separate branches (so-called k-particles branches, k= 0,1,2,…), and with probability one it is a nonrandom set. We find the location of the spectrum and prove the localization for the one-particle branch of the spectrum. As a consequence we find a lower bound for the spectral gap for any realization of the random potential. Received: 22 September 1998 / Accepted: 12 February 1999     

非线性啁啾频率对势阱产生正负电子对的增强

用计算量子场论方法研究了非线性啁啾频率对势阱中正负电子对产生的增强效应。研究了由静态势阱和动态势阱组成的组合势阱中产生的正负电子对的密度、产额和能谱等性质随着啁啾参数的变化,分析了组合势阱的频谱和瞬时束缚态。发现非线性啁啾效应对低频区域比较敏感,与固定频率情况相比可以使粒子数增加2～3倍。与组合势阱相比,非线性啁啾效应对单个振荡势阱更敏感。在低频下单个振荡的势阱中正负电子对产额可提高多个数量级。这是因为在低频下单个振荡的势阱中,主要通过量子隧穿过程产生的正负电子对数目非常低。非线性啁啾效应增加了高频场成分,提高了多光子过程和动力学辅助机制。由于高频抑制作用,所以非线性啁啾效应对高频区域粒子的增量不大,甚至会抑制正负电子对的产生。     

Quark-quark potentials from the inversion of baryon-spectra and its application to the Roper resonance

We show that it is in principle possible to determine the quark-quark potential, in the nonrelativistic potential model, from the baryon spectrum. The method we propose is based on the fact that the lowest order of the hyperspherical-harmonic expansion method, the hypercentral approximation, is an excellent approximation for confining quark-quark potentials. However, our method applies to all cases where this assumption is valid. Using standard inverse spectrum techniques adapted to our problem we invert the baryon spectrum to obtain the hypercentral potential in the hyperradius of the three-quark system. By means of a new exact relation based on the Abel integral equation, we can invert the hypercentral potential to determine the quark-quark potential.A first application of this new method to the inversion of thes-state baryon spectrum demonstrates in a model-independent way the inability of nonrelativistic two-quark potentials to reproduce the Roper resonance without violating the QCD-motivated concavity requirement.Dedicated to Profs. Erich Schmid and Ivo laus on the occasion of their 60th birthdays     

类环型Hulthén势任意分波束缚态的近似解析解简

类环型Hulthén势是Hulthén势外面再加上类环型平方反比势.用指数函数近似表示任意分波的离心项,运用函数分析法讨论类环型Hulthén势Schrdinger方程的束缚态解.归一化的角向波函数和径向波函数用超几何函数表示,给出了束缚态能谱,体系的波函数和束缚态能谱与类环型Hulthén势的势参数和三个量子数有关.Hulthén势、Hartmann势和Makarov势束缚态能谱是类环型Hulthén势的特例.     

Some problems with the hyperfine structure of charmonium

Some intriguing properties are obtained for the charmonium spectrum when the Schrödinger equation is solved with a potential that is a sum of a linear confining and a Coulomb-like term, supplemented by spin-dependent forces derived from the one vector-gluon exchange hypothesis. The results are discussed in light of various possible assignments of quantum-numbers to the experimental ψ and χ states. We conclude that such a potential cannot fit the experimental spectrum.     

Photoassociation Spectroscopy: Determination of Parameters of Potentials of Diatomic Molecules

Laser-induced fluorescence studied with the help of a tunable dye laser is used to record the photoassociation spectrum of equilibrium mercury atoms in the range of 34 700–37 300 cm^–1. The so-called Franck-Condon structure, which represents periodic variations of absorption intensity on a continuous background, is observed. The structure makes it possible to determine spectroscopic parameters of the upper bound potential and the lower repulsive potential, including the potential with a shallow Van der Waals well. The Numerov-Cooley procedure is used to find the numerical solution of the boundary problem, namely, eigenfunctions and eigenvalues of the Schrödinger equation for the one-dimensional motion in a potential field, matrix elements of transitions and partial waves, and the absorption spectrum of collisional pairs of atoms are calculated. The absorption spectrum of mercury dimers was simulated taking into account 100 vibrational and 200 rotational levels. The comparison of theoretical and experimental spectra according to Tellinghuisen made it possible to determine the lower part of the potential curve for the dimer excited state.     

Investigation of one class of Bargman-type potentials

For the spectral problem on the half-axis we derive an expression for the potential with N levels of discrete spectrum that are positioned in a previously determined fashion. We obtain wave functions for the discrete spectrum, Yost’s solution, and the continuous-spectrum functions. We show that the Yost function for this potential is a rational fractional function of the wave number k and, consequently, the potential itself is a potential of Bargman type. Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 34–39, May, 1998.