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。     

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.     

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。     

An effective quantum defect theory for the diamagnetic spectrum of barium Rydberg atom

A theoretical calculation is carried out for the spectrum of barium Rydberg atom in an external magnetic field. Using an effective approach incorporating quantum defect into the centrifugal term in the Hamiltonian, we reexamine the reported spectrum of barium Rydberg atom at a magnetic field of 2.89 T [J. Phys. B 28 L537 (1995)]. Our calculation employs B-spline basis expansion and complex coordinate rotation techniques. For single photon absorption from the ground 6s² to 6snp Rydberg states, the spectrum is not influenced by quantum defects of channels ns and nd. The calculation is in agreement with the experimental observation until the energy reaches E=-60 cm^-1. Up beyond in energy, closer to the threshold, the calculated and experimental results do not agree with each other, possible reasons for their discrepancies are discussed. Our study affirms an energy range where the diamagnetic spectrum of barium atom can be explained thoroughly using a hydrogen model potential.     

An effective quantum defect theory for the diamagnetic spectrum of a barium Rydberg atom

A theoretical calculation is carried out to investigate the spectrum of a barium Rydberg atom in an external magnetic field. Using an effective approach incorporating quantum defect into the centrifugal term in the Hamiltonian, we reexamine the reported spectrum of the barium Rydberg atom in a magnetic field of 2.89 T [J. Phys. B 28 L537 (1995)]. Our calculation employs B-spline basis expansion and complex coordinate rotation techniques. For single photon absorption from the ground 6s2 to 6snp Rydberg states, the spectrum is not influenced by quantum defects of channels ns and nd. The calculation is in agreement with the experimental observations until the energy reaches E = 60 cm-1 . Beyond this energy, closer to the threshold, the calculated and experimental results do not agree with each other. Possible reasons for their discrepancies are discussed. Our study affirms an energy range where the diamagnetic spectrum of the barium atom can be explained thoroughly using a hydrogen model potential.     

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.     

长脉冲激光场中H原子的阈上电离的理论研究

利用基于密度泛函理论下的窗算符技术求解含时薛定谔方法计算了H原子在长脉冲强激光场中能量谱, 并与文献[8]中的动量空间的投影技术方法的计算结果进行了比较。在文献[8]给出的最大光电子能量范围内,我们的计算结果与文献[8]中的计算结果符合得很好,但是我们的计算结果能够给出比文献[8]中能量更高的光电子能谱,光电子能量谱的变化趋势也与实际的物理过程相符。同时我们也给出了最大光电子能量与激光强度关系的经验公式,利用我们的经验公式计算的最大光电子能量与经典计算预测的最大光电子能量符合得很好,这表明们的计算方法可靠,能够给出高精度的计算结果。因此利用基于密度泛函理论下的窗算符方法能很好地用来研究H原子在长脉冲强激光场中的阈上电离的性质。     

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.     

Quantized magnetic flux through the ground-state orbit of the hydrogen atom

We have investigated the spin-dependent quantized magnetic fluxes through the ground-state electronic orbit of the hydrogen atom. We show that the corresponding fluxes are (1/2)Φ₀ for the spin-up case and (3/2)Φ ₀ for the spin-down case, respectively, where Φ₀ = hc/e is the flux quantum. Using the energy-flux proportionality, we also show that the spin-up case (where the electron spin is antiparallel to the proton spin, resulting in zero total spin) is the spin-dependent ground state of the hydrogen atom. The present result helps to understand the spin flip-flop in excitonic transitions in nanostructures.     

均匀磁场中氢原子低能级简并度的解除

讨论了均匀强磁场中氢原子哈密顿量中B^2项的影响，指出在忽略自旋－轨道相互作用的情况下，该项可使氢原子低能级简并度完全解除。     

Singular continuous spectrum on a cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian

It is rigorously proven that the spectrum of the tight-binding Fibonacci Hamiltonian,H _mn= _{m, n+1}+ _{m, n–1}+ _{m, n} [(n+1)]–[n]) where =(5–1)/2 and [·] means integer part, is a Cantor set of zero Lebesgue measure for all real nonzero, and the spectral measures are purely singular continuous. This follows from a recent result by Kotani, coupled with the vanishing of the Lyapunov exponent in the spectrum.On leave from the Central Research Institute for Physics, Budapest, Hungary.