氢原子问题的试探解法

本文给出一种初等解法（试探解法）,用以求出氢原子束缚态的定态波函数及能量、角动量平方与角动量第三分量的量子化条件     

受限氦原子的共振增强现象

本文用B样条方法计算了受限氯原子的能级与波函数,并在此基础上研究了氯原子的跃迁谱特性,发现了在限制势的作用下,氯原子跃迁谱有非常强的共振增强现象出现。     

受限氦原子的共振增强现象

本文用B样条方法计算了受限氦原子的能级与波函数,并在此基础上研究了氦原子的跃迁谱特性,发现了在限制势的作用下,氦原子跃迁谱有非常强的共振增强现象出现.     

氢原子的多光子共振电离

线极化光场下氢原子Ｓｃｈｒｄｉｎｇｅｒ方程,可以迭代方法求解,并用电离问题边界条件,求复本征值,由此可得到多光子共振电离公式,并与实验比较     

氢原子径向波函数的“初等”解法

用构造氢原子径向波函数的方法,通过解薛定谔方程给出氢原子径向波函数幂多项式的系数．     

高对比度透射光谱中碰撞增强的Hanle共振

在高对比度透射光谱中观察到线宽18mG(FWHM)钠原子基态中碰撞增强的Hanle共振.此共振的线宽仍表现出Dicke变窄效应,但信号的强度却随着缓冲气体压强急剧地增加.     

一维模型氢原子在啁啾激光场中的阈上电离

通过数值求解一维模型氢原子在啁啾激光场中的含时薛定谔方程,研究了在不同电离机制下啁啾率对阈上电离能谱的影响. 计算结果表明,三种不同电离区域的光电子能谱对啁啾率的依赖程度不同. 结合激发束缚态的总布局,阐明了多光子阈上电离能谱的啁啾依赖主要源自于激发束缚态的贡献. 而单光子和隧穿电离区,电子可通过吸收单个光子或隧穿势垒到达连续态,因此激发束缚态的影响较小. 另外,隧穿电离区光电子能谱第一个平台截止位置对啁啾率的依赖可归结于激发束缚态的贡献.     

广义Woods-Saxon势的转移共振

本文严格求解了一维广义Woods-Saxon势的薛定谔方程,导出了用超几何函数表达的散射态波函数,获得了转移和反射系数的解析表达式。利用波函数的连续性条件,计算了在广义Woods-Saxon势中运动粒子的转移和反射系数。特别地,详细分析了转移共振和广义Woods-Saxon势的参数关系,展示了发生转移共振的条件。     

广义Woods-Saxon势的转移共振

本文严格求解了一维广义Woods-Saxon势的薛定谔方程,导出了用超几何函数表达的散射态波函数,获得了转移和反射系数的解析表达式。利用波函数的连续性条件,计算了在广义Woods-Saxon势中运动粒子的转移和反射系数。特别地,详细分析了转移共振和广义Woods-Saxon势的参数关系,展示了发生转移共振的条件。     

强激光场中H-离子二维光电子动量谱的理论研究

选用两个模型势,利用强场近似方法研究了H-离子在线性极化强激光场中二维光电子动量谱中次外层后重散射环.研究结果表明:两个模型势中的极化势对二维光电子动量谱的影响很小;随着激光强度的增加,二维光电子动量谱中出现后重散射环的数目变多,沿着次外层后重散射环的光电子的角分布波动性变小,能够通过多项式拟合的方法从二维光电子动量谱中次外层后重散射环获得精确的电子与H原子的弹性散射截面,特别适用于激光强度较小的情况.     

用Coulomb-Volkov方法研究强激光场中H原子的电离

利用Coulomb-Volkov方法研究了H原子在不同波长的线性极化强激光场中电离的能量谱和动量谱,并与强场近似和直接数值求解含时Schr(o|¨)dinger方程的结果进行比较,结果发现:随着激光频率的增加,由Coulomb-Volkov方法得到的结果与数值求解含时Schr(o|¨)dinger方程的结果符合得很好.     

Appearance of a purely singular continuous spectrum in a class of random schrödinger operators

We consider a discrete Schrödinger operator on l²() with a random potential decaying at infinity as ¦n¦^–1/2. We prove that its spectrum is purely singular. Together with previous results, this provides simple examples of random Schrödinger operators having a singular continuous component in its spectrum.     

Stability Criteria for the Weyl m-Function

This paper presents a new approach to spectral theory for theSchrödinger Operator on the half-line. Solutions of nonlinearRiccati-type equations related to the Schrödinger equation at realspectral parameter are characterised by means of their clusteringproperties as is varied. A family of solutions exhibiting aso-called -clustering property is shown to imply precise estimatesfor the complex boundary value of the Weyl m-function and thespectral measure, and leads to an analysis of the absolutely continuouscomponent of the spectral measure in terms of stability criteria for thecorresponding Riccati equations.     

An Example of Embedded Singular Continuous Spectrum for One-Dimensional Schrödinger Operators

We present a new example of a potential such that the corresponding Schrödinger operator in the halfaxis has singular continuous spectrum embedded in the absolutely continuous spectrum. The singular part is supported in an essentialy dense set. This generalizes a result of C. Remling [3].Mathematics Subject Classification: 34L40, 81Q10.     

On the existence of hydrogen atoms in higher dimensional Euclidean spaces

The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions (D) greater than 3 is revisited. The lowest quantum mechanical stable states and the corresponding wave functions are determined by applying Numerov?s method to solve Schrödinger?s equation. States for different angular momentum quantum number and dimensionality are considered. One is lead to the result that hydrogen atoms in higher dimensions could actually exist. The most probable distance between the electron and the nucleus are then computed as a function of D showing the possibility of tiny confined states.     

On the Essential Spectrum of Two-Dimensional Periodic Magnetic Schrödinger Operators

For two-dimensional Schrödinger operators with a nonzero constant magnetic field perturbed by an infinite number of periodically disposed, long-range magnetic and electric wells, it is proven that when the inter-well distance (R) grows to infinity, the essential spectrum near the eigenvalues of the one well Hamiltonian is located in mini-bands whose widths shrink faster than any exponential with R. This should be compared with our previous result, which stated that, in the case of compactly supported wells, the mini-bands shrink Gaussian-like with R.     

Schrödinger Operators with Empty Singularly Continuous Spectra

Let H be a semibounded perturbation of the Laplacian H ₀ in L ²( ^d ). For an admissible function sufficient conditions are given for the completeness of the scattering system (H), (H ₀). If is the exponential function and if e^{– H} is an integral operator we denote the kernel of the difference D = e^{– H} – e^{– H} ₀ by D (x, y), > 0. The singularly continuous spectrum of H is empty if^d dx ^d dy |D(x,y)| (1 + |y|²)< for some > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions.     

Singular Continuous Spectrum for a Class of Substitution Hamiltonians II

We consider discrete one-dimensional Schrödinger operators with aperiodic potentials generated by primitive substitutions. Using the three-block version of Gordon's criterion, we establish purely singular continuous spectrum with probability one provided that the potentials have index greater than three. It is also shown that one cannot use this criterion to prove uniform results.     

Optical solitons in (1 + 1) and (2 + 1) dimensions

This paper addresses the nonlinear Schrödinger's equation that serves as the model to study the propagation of optical solitons through nonlinear optical fibers. The main focus of this paper is the aspect of integrability. There are a couple of integration tools that are employed to obtain the exact solutions to the model. Fan's F-expansion approach is applied to extract several forms of solutions to the model. This integration mechanism displays cnoidal waves, snoidal waves and several other solutions; needless to mention that these solutions, in the limiting case, leads to bright, dark and singular soliton solutions. The study then rolls over to the (2 + 1)-dimensions where, in addition, the semi-inverse variational principle is applied to extract a bright soliton solution, along with the necessary constraint conditions. There is also a display of several numerical simulations.     

Symplectic Structures for the Cubic Schrödinger Equation in the Periodic and Scattering Case

We develop a unified approach for construction of symplectic forms for 1D integrable equations with the periodic and rapidly decaying initial data. As an example we consider the cubic nonlinear Schrödinger equation. Mathematics Subject Classifications (2000) 35Q53, 58B99.The work is partially supported by NSF grant DMS-9971834.