共查询到19条相似文献,搜索用时 78 毫秒
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各向同性谐振子是量子理论中能够严格求解的可解势场之一.对它的研究和讨论,在理论上和实际的应用中都有重要意义.本文推导出了N维(N≥2)各向同性谐振子径向矩阵元〈nrl|rk|nr′l′〉的递推公式,在此基础上得到了平均值的递推公式,并且讨论了维各向同性谐振子径向矩阵元的递推公式的一般性,而文献[3]与[4]所给出的各向同性谐振子径向矩阵元的递推公式只是本文结论的特例. 相似文献
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环形振子径向矩阵元的通项表达式及其递推关系 总被引:1,自引:0,他引:1
利用文献1给出的环形振子的归一化的径向波函数,推导出环形振子径向矩阵元的通项表达式及其递推关系.解决了环形振子径向矩阵元的计算问题. 相似文献
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提出了一种新的精确可解的三维解析势函数,即环形非球谐振子。势函数为V(γ,θ)=1/2mω^2γ^2 h^2/2mA/γ^2 h^2/2mb/γ^2sin^2θ。将环形非球谐振子势的Schroedinger方程在球坐标系中进行变量分离,得到了角向方程和径向方程,给出了精确的能谱方程,获得了用普遍的associated-Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数。球谐振子、非球谐振子和环形振子的有关结果均作为特例包含在本文的一般结论之中。 相似文献
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利用新环形库仑势的归一化的束缚态径向波函数和按“k/2π标度”归一化的散射态径向波函数,本文给出了新环形库仑势的任意幂次的束缚连续跃迁矩阵元的通项表达式.为了简化高幂次的束缚连续跃迁矩阵元的计算,我们还推导出了不同幂次的束缚连续跃迁矩阵元之间所满足的递推关系,并提出了计算径向波函数微商的矩阵元的计算办法.本文结果可广泛的用于原子与分子的散射问题特别是环形分子的散射问题之中. 相似文献
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利用谐振子径向波函数的渐近行为和积分特性,导出了谐振子径向幂坐标矩阵元〈n′_rl′|r~k|n_rl〉的递推关系,从而把有关文献中关于对角元〈n_rl|r~k|n_rl〉的递推关系推广到更为一般的形式。 相似文献
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根据广义Laguerre多项式的数学性质,导出了较为简单的三维各向同性谐振子径向矩阵元的普遍公式,并在这基础上计算了一些重要特殊情形的径向矩阵元: 矢径r整数次幂的平均值,电偶极跃迁矩阵元和电四极跃迁矩阵元.
关键词:
三维各向同性谐振子
径向矩阵元
广义Laguerre多项式
偶极跃迁
四极跃迁 相似文献
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获得了球谐振子径向算符r2s正偶次幂和负偶次幂平均值之间的一个递推关系,在-4s4情况下给出了平均值<nrl|r2s|nrl>的解析计算结果. 相似文献
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For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ j N =1 (x j ? 〈x〉) is computed exactly and shown to satisfy a central limit theorem asN → ∞. For the circular random matrix ensemble the p.d.f.’s for the statistics ½Σ j N =1 (θ j ?π) and ? Σ j N =1 log 2 |sinθ j/2| are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem asN → ∞. 相似文献
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In this paper, we study variation formulas for transversally harmonic and biharmonic maps, respectively. We also study the transversal Jacobi field along a map and give several relations with infinitesimal automorphisms. 相似文献
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Accuracy of the Kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. Disagreement between the Kramers rate and the dynamical one is shown to reach 15% in the cases when much better agreement is expected. Corrections to the Kramers formulas accounting for the higher derivatives of the potential are obtained. The small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential. The distance between the potential barrier and the absorptive border is accounted for as well. This corrected Kramers rate is demonstrated to agree with the dynamical rate typically within 2%. Probably the most interesting result is that despite the corrections are derived in the case of the overdamped Brownian motion, the above 2% agreement holds even in the case of medium friction. 相似文献
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通过分析指出:电磁场是一个不可分割的整体,Maxwell方程组是电磁场的运动方程,电磁场的源是电荷与电流的分布,Jefimenko公式是真空中Maxwell方程组的解。 相似文献
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Explicit expressions and recurrence formulas of radial average value for N-dimensional hydrogen atom
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Itiswellknownthattheclassofanalyticallysolublesystemsinquantummechanicsinlimited ,N dimensionalhydrogenatomisoneoftheexactsoluble 相似文献
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Howard Weiss 《Journal of statistical physics》1992,69(3-4):879-886
We derive several variational formulas for the topological entropy and SRB entropy of Axiom A flows on compact manifolds and for the Hausdorff dimension of basic sets for Axiom A diffeomorphisms on compact surfaces. 相似文献
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给出了相对论性无自旋氢原子的解析波函数,推导出了计算径向矩阵元的通项公式.在-6≤s≤3的条件下,给出了径向平均值〈n′l′|rs|n′l′〉的解析表达式. 相似文献
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In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived. 相似文献