共查询到19条相似文献,搜索用时 453 毫秒
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三维各向同性q变形振子的双波描述 总被引:2,自引:1,他引:1
利用双波函数理论描述三维各向同性q变形振子力学量随时间的演化方程,结果显示粒子做非线性振动.同时,当r→0时,所有结论退化为普通三维各向同性谐振子的相关结果. 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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文中得到d维各向同性谐振子归一化径向波函数. 在径向基本算子r,(1)/(r),(d)/(dr)的基础上,可以直接构造d维各向同性谐振子的四类升降算子,同时也得到它们的归一化系数. 相似文献
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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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研究带电粒子在均匀磁场与三维各向同性谐振子场中运动的双波描述,得到了量子结果及其 经典极限,并与纯经典情形比较.
关键词:
双波描述
均匀磁场
谐振子场 相似文献
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As a nonrelativistic particle constrained to remain on an(N?1)-dimensional((N≥2))hypersurface embedded in an N-dimensional Euclidean space,two different components pi and pj(i,j=1,2,3,...N)of the Cartesian momentum of the particle are not mutually commutative,and explicitly commutation relations[p^i,p^j](≠0) depend on products of positions and momenta in uncontrollable ways.The generalized Dupin indicatrix of the hypersurface,a local analysis technique,is utilized to explore the dependence of the noncommutativity on the curvatures around a local point of the hypersurface.The first finding is that the noncommutativity can be grouped into two categories;one is the product of a sectional curvature and the angular momentum,and another is the product of a principal curvature and the momentum.The second finding is that,for a small circle lying a tangential plane covering the local point,the noncommutativity leads to a rotation operator and the amount of the rotation is an angle anholonomy;and along each of the normal sectional curves centering the given point the noncommutativity leads to a translation plus an additional rotation and the amount of the rotation is one half of the tangential angle change of the arc. 相似文献
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We show that the HERA data for the inclusive structure function F2(x,Q2) for x10−2 and 0.045Q245 GeV2 can be well described within the color dipole picture, with a simple analytic expression for the dipole–proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Qs(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Qs(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x0 of x at which the saturation scale Qs equals 1 GeV, and the logarithmic derivative of the saturation momentum λ. The value of λ extracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism. 相似文献
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电非对称效应作为一种新兴技术,被广泛用于对离子能量和离子通量的独立调控.此外,在改善等离子体的径向均匀性方面,电非对称效应也发挥了重要作用.本文采用二维流体力学模型,并耦合麦克斯韦方程组,系统地研究了容性耦合氢等离子体中当放电由多谐波叠加驱动时,不同谐波阶数k下的电非对称效应,重点观察了相位角θn对自偏压以及等离子体径向均匀性的影响.模拟结果表明:在同一谐波阶数下,自偏压随相位角θn的变化趋势不尽相同,且当k增大(k>3)时,自偏压随最高频相位角θk的变化范围逐渐减小.此外,通过调节相位角θn,可以改变轴向功率密度和径向功率密度的相对关系,进而实现对等离子体径向均匀性的调节.研究结果对于利用电非对称效应优化等离子体工艺过程具有一定的指导意义. 相似文献
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Magnetic characteristics of Ti-, Zr- and Hf-substituted PrCo5 alloys have been studied over the temperature range from 77 to 300 K and for applied fields up to 20 kOe. It is established that Ti, Zr and Hf substitute for Pr. Single-phase materials are formed for all values of x up to 0.2 in the system Pr1−xZrxCo5 but for x only up to 0.1 for Pr1−xTix Co5 and Pr1−xHfxCo5 alloys. Larger amounts of Zr can be substituted if the material is made hyperstoichiometric in Co, e.g., Pr0.7Zr0.3Co5.5. All the alloys show a decrease in magnetic moment and an increase in Curie temperature as x increases. Anisotropy fields decrease as x increases at 295 K. Anomalous behavior is observed at 77 K, suggested that these ternary alloys may have a cone structure at this temperature. 相似文献
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We exhibit and discuss the QCD prediction for the transverse momentum distribution of W bosons, Z bosons and high-mass virtual photons produced in high-energy hadron-hadron collisions. Recent work has shown that this prediction is consistent with the structure of leading twist initial state interactions.
The expression we present is expected to give results correct up to order sN(Q) for any QT when the boson mass Q is very large (> 108 GeV!), given only input from perturbative calculations at order sN+2 and deeply inelastic scattering structure functions. We specify the required N = 0 coefficients, employing the order s2 results of Kodaira and Trentadue and of Davies and Stirling. We then show how the expression should be modified to deal with current energy scales. We also discuss the connection between low-QT and high-QT formulae. 相似文献
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The Einstein equations for rotating axisymmetric configurations in asymptotically flat spacetimes are put in a form suitable for numerical calculations of dynamics. The discussion is motivated by the astrophysical problem of gravitational collapse with generation of gravitational radiation and possibly black hole formation. In the context of topologically spherical coordinates there are two spatial gauge conditions which greatly simplify the Einstein equations and are compatible with regularity at the origin. We focus on one, the radial gauge, which generalizes Schwarzschild coordinates and is asymptotically a transverse-traceless gauge for gravitational radiation. The shift vector equation and the Hamiltonian constraint are parabolic equations in the radial gauge, rather than the usual elliptic equations. Two hypersurface conditions are explored in detail, the maximal hypersurface condition and another “polar” hypersurface condition which fits naturally with the radial gauge. 相似文献
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Qian Dong Ariadna J. Torres-Arenas Guo-Hua Sun Wen-Chao Qiang Shi-Hai Dong 《Frontiers of Physics》2019,14(2):21603
In this work we analyze the characteristics of quantum entanglement of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity NABI (ρTAABI) increases with F but decreases with the variable y, while the variation of the negativity NBIBII(ρTAABI) is opposite to that of the negativity NABI (ρTAABI). We also study the von Neumann entropies S(ρABI) and S(ρBIBII). We find that the S(ρABI) increases with variable y but S(ρBIBII) is independent of it. However, both S(ρABI) and S(ρBIBII) first decreases with F and then increases with it. The concurrences C(ρABI) and C(ρBIBII) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it. 相似文献
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本文提出了予测稠苯芳杂环及其烷基链上质子化学位移的计算方法。
将稠苯芳杂环化合物用凯库勒式表示,计算式为为需考虑的苯环内的乙烯基效应。σmi,ci为各苯环的环流效应。σ1,Hc为各芳杂环的屏蔽效应,对杂环上质子它就是该单独芳杂环上相应质子的δ值,对苯环上质子要将它分解为各结构因素的效应,即:σ1,He=(1/2)d-1δx=y(或σz)+σc-c·σm,H.
σx-y与σz为杂原子或其基团的屏蔽效应,σc=c为存在于芳杂环中的乙烯基的效应,σm,Hc为芳杂环的环流效应,d为对不同质子所考虑的键数。有取代基时需考虑取代基的效应。计算环上烷基质子的公式为:δ=σp,CH3+ασc,CH3+βσt,CH3+σl,G
σl,G为稠苯芳杂环基的某级效应。 相似文献