强磁场中氢原子自离化态的能级及宽度

使用Bsplines与复坐标旋转相结合的方法计算了均匀外磁场(2.35×10~6≤B≤1.175×10~4T)中氢原子│m│=0—5,偶宇称和奇宇称自离化态的能级和宽度.并与已有的结果作了比较.分析了共振态能级位置和宽度与态的宇称、磁量子数│m│及磁场强度的关系.结果表明:Bsplines与复坐标旋转方法相结合可以有效地用于强外场中原子自离化态的计算. 关键词：     

压缩真空变态中二能级原子简并双光子过程的广义Bloch—Siegert频移

用密度算符主方程方法研究了一二能极原子与宽压缩真空态光场的简交双光子相互作用。我们发现原子偶极矩随时间的变化与压缩真空态光场的压缩参数│Ｍ│有关。│Ｍ│存在一个阈值Г／４ｇ。阈值之下，原子偶极矩以共振频率振荡。     

共下能级双跃迁激光的量子理论

本文将Sargent,Scully和Lamb的二能级单模激光全量子理论推广到共下能级三能级双模激光系统中,获得了三个能级都有泵浦情况下的共下能级三能级原子系统双模激光运转的主方程。考虑到细致平衡与宏观平衡之间的对应性,合理地应用细致平衡原理得到定态运动方程。通过引入一个参数H,从而获得了形式解。利用运动方程和形式解,讨论了不同条件下的一些运转特性和光子统计分布的变化.     

941nm大功率应变单量子阱激光器的波长设计

从薛定谔方程出发推导了阶梯形有限深应变单量子阱中的特征值方程，研究了台阶宽度对激射波长、电子第一子能级、空穴第一子能级的影响以及空穴第一子能级对激射波长的影响，计算结果表明当有源区In组分较大时，不能忽略空穴第一子能级对激射波长的影响.该模型计算结果与实验值相吻合. 关键词： 薛定谔方程 有限深势阱 应变量子阱 特征值方程     

弱电场下Stark能级的近似计算法

恒定外电场下，类氢原子的Ｓｃｈｒｏｄｉｎｇｅｒ方程可在抛物座标下分离变量，然后求解。渐过波函数的几率振幅极小值定义了Ｓｔａｒｋ能级，在弱电场情形，本文讨论了一种近似计算法。     

Airy传递矩阵法与偏压下多势垒结构的准束缚能级

使用Airy函数和传递矩阵方法精确计算了一维定态薛定谔方程，并推广到多势垒结构，求解出有/无偏压作用的2,3势垒结构的准束缚能级，进一步研究了有/无偏压作用的2,3势垒结构的准束缚能级与有效质量和外加电压的关系，并对结论的正确性进行了验证． 另外，文中 还指出了有些文章中关于Airy传递矩阵法与计算偏压下多势垒结构的准束缚能级的错误陈述 . 关键词： 准束缚能级 有/无偏压作用的多势垒结构 Airy函数 透射系数     

一维多量子阱的能级

给出了一维多量子阱能级满足的超越方程,利用此方程可以求出任意一维势的束缚态能级．     

对于计算能级占据数密度的速率方程的一些讨论

本文讨论了通常计算能级占据数时所用的平均离子模型中引进的近似。给出了改进的高一阶近似的方程系;证明了在电偶极近似下能级占据概率P_(nlj)与量子数j无关,这样求解的方程数可大大减少;最后,提出了一种可行的解速率方程的方法。     

求解径向Schroedinger方程解析解的一种方法以及由此延伸的讨论—叠加势基态能级与势参数关系

采用转化法，可得到一系列具有球对称势函数的径向Schroedinger方程的解析解和能级方程。这种方法是用一个恰当的尝试波函数代入Schroedinger方程后，将微分方程变成简单的可解的代数方程组，由此大大简化了运算。本给出了库仑势、库仑势与谐振子势的叠加势以及离子与原子相互作用势的径向Schroedinger方程解析解，并得到能级方程。由于此方法中涉及一个势参数制约关系，为此以叠加势V(r)=-A1r^-1-A2R^-3 A3r^-4为例，讨论其基态能级。得出重要结论：在库仑势上叠加上两项逆幂指数势作用后基态能量将增大，但是并不是单调增大，而是与各项势参数有关。     

不均匀垂直磁场中偏压AA堆积双层石墨中的朗道能谱

本文从量子力学的基本概念出发,在对称规范变换下,借助特殊函数方程理论,研究了不均匀磁场和垂直电场联合作用下AA堆积双层石墨的朗道能级结构.结果表明该体系中的朗道能级是高度简并的,特别是在狄拉克点处,而且该体系中偶然简并的零能朗道能级能够被垂直电场有效地调控.     

Semi-exact Solutions of Konwent Potential

In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1).     

Surface relaxation of Pt(111) investigated by ion scattering

The energy levels of some specific forms of screened Coulomb potential, as a function of the perturbation parameter λ, are shown to have a branch cut along the negative real axis, and singularities on the second sheet along $\text{|λ| e}{}^{\mathrm{<mtext>\pm (</mtext><mtext>3</mtext><mtext>2</mtext><mtext>)i\pi </mtext>}}$ for |λ| → 0. As a consequence, the energy levels have an asymptotic series in λ, which cannot be used to describe the energy levels to an arbitrary accuracy.     

锶蒸气M-M跃迁激光

通过在锶蒸气和氦混合气体中的高重复率脉冲放电,同时获得了锶原子4条谱线的激光振荡,它们对应于复三能级4d·³D_3,2,1与5p·³P⁰_2,1,0之间的多谱线跃迁,其波长分别为292μm,301μm,269μm和260μm.除了301μm激光外,均为首次报道.激光平均功率合计约10mW,相互之间的强度比为5∶4∶4∶1.在分析了相关能级特征和实验现象的基础上,对其作用机理进行了初步的探讨,建议将其分 关键词： 锶蒸气激光 自终止 M-M跃迁     

Explicit Relations of Physical Potentials Through Generalized Hypervirial and Kramers' Recurrence Relations

Based on a Hamiltonian identity,we study one-dimensional generalized hypervirial theorem,Blanchardlike(non-diagonal case) and Kramers'(diagonal case) recurrence relations for arbitrary x~κ which is independent of the central potential V(x).Some significant results in diagonal case are obtained for special κ in x~κ(κ≥ 2).In particular,we find the orthogonal relation(n_1|n_2) = δ_(n_1n_2)(κ = 0),(n_1|V'(x)\n_2) =(E_(n_1)-E_(n_2))~2〈n_1x|n_2)(κ = 1),E_n =(n/V'(x)x/2|n) +(n|V(x)|n)(κ = 2) and-4E_n(n|x|n) +(n|V'(x)x~2\n〉 +4〈n|V(x)x|n〉 = 0(κ = 3).The latter two formulas can be used directly to calculate the energy levels.We present useful explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.     

|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

1 Introduction Though one-dimensional (1D) systems may clearly exhibit many features of quan-tum mechanics, systems with many degrees of freedom provide more opportunities tostudy many other important features, e.g. the degeneracy of energy eigenstates, whichneed a complete set of commuting observables to characterize an energy eigenstate. Inparticular, two-dimensional (2D) systems with two spatial degrees of freedom may ex-hibit symmetries not present in 1D systems, e.g. the rotational symme…     

Circular Rydberg States of Atomic Hydrogen in an ArbitraryMagnetic Field

We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy of circular Rydberg states of hydrogen atoms in the intermediate magnetic field. This scheme can produce high accuracy energy levels and valid for an arbitrary magnetic field. Energy levels of hydrogen are presented for circular Rydberg states with azimuthal quantum numbers |m| = 10--70 as a function of magnetic field strengths ranging from zero to2.35
ⅹ10⁹ T. The variation of spatial distributions of electron probability densities with magnetic field strengths is discussed and competition between Coulomb and magnetic interactions is illustrated.     

Approximate Selection Rules for |K| = 1-0 and 1-1 Tunneling-Rotation Transitions in the Methanol Dimer

Approximate K = 0 and |K| = 1 tunneling-rotation eigenfunctions for the four A, four E, and one G symmetry species present in the methanol dimer, derived from molecular parameters obtained previously from a least-squares fit to transition frequencies involving K = 0 and 1 levels, are used to clarify some apparent contradictions associated with traditional b- and c-type transition designations in the E and G tunneling-rotational states of this dimer. These approximate eigenfunctions also predict strong and weak line intensities which are consistent with the pattern of strong a-, b-, and c-type transitions observed, thus supporting our previous separate K-state analysis based only on energy level differences. Some of the predicted weaker |K| = 1 a-type transitions should be experimentally observable with more signal averaging. Copyright 2000 Academic Press.     

Josephson effect between nanoclusters in resonance conditions

A general expression is derived for the Josephson current between nanoclusters. It is shown that, in the resonance conditions between electron levels of clusters, the expression for the current obtained in the tunnel Hamiltonian model becomes invalid. In the case of degeneracy or close to degeneracy of energy levels in isolated clusters, the critical Josephson current may exceed the value obtained in the model of tunnel Hamiltonian in the large parameter, viz., the ratio of the order parameter |Δ| to the distance between the resonance level and the levels closest to it.     

Generalized Random Energy Model II

The formulae for the free energy, when the driving distributions in Generalized Random Energy Model (GREM) are of the form for γ ≥ 1 are derived. The large deviation technique allows the use of different distributions at different levels of the GREM. As an illustration we consider, in detail, a two level GREM with exponential and Gaussian distributions. This simple case itself leads to interesting phenomena.     

Dark matter and dark energy from the solution of the strong CP problem

The Peccei-Quinn (PQ) solution of the strong CP problem requires the existence of axions, which are viable candidates for dark matter. If the Nambu-Goldstone potential of the PQ model is replaced by a potential V(|Phi|) admitting a tracker solution, the scalar field |Phi| can account for dark energy, while the phase of Phi yields axion dark matter. If V is a supergravity (SUGRA) potential, the model essentially depends on a single parameter, the energy scale Lambda. Once we set Lambda approximately equal to 10(10) GeV at the quark-hadron transition, |Phi| naturally passes through values suitable to solve the strong CP problem, later growing to values providing fair amounts of dark matter and dark energy.