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laguerre函数
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  laguerre function
    In consideration of the factor that the energy of the induced current on a scattering object excited by a plane wave with a Gaussian pulse almost all concentrates on a finite time and frequency-domain, by expanding the response in time with Laguerre function, a corresponding frequency-domain response is attained by using Fourier transform.
    考虑到散射体在高斯脉冲平面波激励下感应电流的能量几乎全部集中在有限时间和频率的范围内这一因素,将时域响应用Laguerre函数展开,并由傅里叶变换,可得到相应的频域响应。
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  “laguerre函数”译为未确定词的双语例句
    The matrix elements of potentials and the involved hyperangle functions are analyticallyexpressible in the linear combination of Saalschutzian hypergeometry function, 4F3(A, B, C, D ;E,F, C ; 1 ).
    再利用广义Laguerre函数展开法对其求解,从而得到一广义能量本征方程,给出了库仑势及有关超球角函数在非对称九维超球谐之间矩阵元的简单解析式,可由一起几何函数4F3:(A,B,C,D;E,F,G;1)的线性组合表示。
短句来源
    The result shows that the method presented here is an effective improvement on the HH-GLF method.
    结果表明本文给出的方法是对直接超球谐广义Laguerre函数展开法(HH-GLF)的一个非常有效的改进。
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  laguerre function
The Laguerre function and the radial Coulomb wave function are defined by their recursion relations.
      
An addition theorem for the Laguerre function is re-derived using these techniques.
      
The characteristics of the principal modes and the multi-input threshold device can be derived from Laguerre function expansions of the computed first- and second-order Volterra kernels when the system is stimulated with a randomly varying input.
      
The new function is a generalization of the q-Laguerre function and the Stieltjes-Wigert function.
      
Finally, limq→1Anα((1 - q)x, -β, 1;q) gives Ln(α,β)(x,q), which is a β-modification of the ordinary Laguerre function.
      
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The wavefunction of the lithium ground -state is decomposed into a product of the two factors, i. e ψ=XΦ, in which X=exp[ - α(r1 +r2+r3)] and Φ is expended in the symmetric basis funtions projected from nine-dimensional hyperspherical harmonics for the two dimensional irreducible representation of S3 permutation group. The Schrodinger equation is reduced into a coupled hyperradial differential equation, and then is directly solved by the generalized Laguerre function expansion method to derive a generalized...

The wavefunction of the lithium ground -state is decomposed into a product of the two factors, i. e ψ=XΦ, in which X=exp[ - α(r1 +r2+r3)] and Φ is expended in the symmetric basis funtions projected from nine-dimensional hyperspherical harmonics for the two dimensional irreducible representation of S3 permutation group. The Schrodinger equation is reduced into a coupled hyperradial differential equation, and then is directly solved by the generalized Laguerre function expansion method to derive a generalized eigen equation of energy.The matrix elements of potentials and the involved hyperangle functions are analyticallyexpressible in the linear combination of Saalschutzian hypergeometry function, 4F3(A, B, C, D ;E,F, C ; 1 ). The eigenenergy better than Hartree-Fock precision for the lithium ground-state 12S is obtained only by taking into account the subset (l1=l2=l3=0) of the complete set of nine-dimensional hyperspherical harmonics. The result shows that the method presented here is an effective improvement on the HH-GLF method.

将Li原子2S态的波函数分解为两项之积,ψ=XΦ,X=exp[-α(r1+r2+r3)],而Φ向以九维超球谐为投影函数而构造的S3置换群的二维不可约表示的基函数展开。Schrodinger方程转化为一起球径耦合微分方程。再利用广义Laguerre函数展开法对其求解,从而得到一广义能量本征方程,给出了库仑势及有关超球角函数在非对称九维超球谐之间矩阵元的简单解析式,可由一起几何函数4F3:(A,B,C,D;E,F,G;1)的线性组合表示。取超球谐函数的子集(l1=l2=l3=0),基态12S的本征能量在超球角方向的收敛速度加快,首次用非变分法得到了优于Hartree-Fock精度的基态能量。结果表明本文给出的方法是对直接超球谐广义Laguerre函数展开法(HH-GLF)的一个非常有效的改进。

Three simple spatially symmetric correlation functions exp[-α(r1+r2+r3)](variable parameter a by E+3/2α2=0,constant α,2.76 and the nuclear charge z,respectively)are used to carry out the correlation-function hyperspherical-harmonic and generalized-Laguerre-function(CFHHGLF)calculations of the ground state lithium atom.With 215 symmetric bases of the two-dimensional irreducible representation for the permutation group S3,constructed from nine-dimensional hyperspherical harmonics,the CFHHGLF calculations provide...

Three simple spatially symmetric correlation functions exp[-α(r1+r2+r3)](variable parameter a by E+3/2α2=0,constant α,2.76 and the nuclear charge z,respectively)are used to carry out the correlation-function hyperspherical-harmonic and generalized-Laguerre-function(CFHHGLF)calculations of the ground state lithium atom.With 215 symmetric bases of the two-dimensional irreducible representation for the permutation group S3,constructed from nine-dimensional hyperspherical harmonics,the CFHHGLF calculations provide the best eigenenergy of-7.473 122 a.u.as α=z,followed by α=2.76,-7.450 788 a.u.,and the variable parameter α,-7.413 668 a.u.,while from the convergence rate in the hyperradial direction,the variable parameter α generates the fastest convergence eigenenergy,and as α=.76 the eigenenergy slowly converges,as α=z the eigenenergy converges only when over 100 symmetry bases are taken into account.In view of the accuracy as well as the stability of the eigenenergy,symmetric exponent correlation function with α=z should be considered to obtain high precise eigenenergy in hyperspherical harmonic method.

在超球坐标下,由3个对称相关函数exp[-α(r1+r2+r3)](α分别为,2.76和核电荷数z),利用相关函数-超球谐-广义Laguerre函数方法(CFHHGLF)直接求解Li原子的Schrdinger方程,计算基态本征能。从数值来看,α=z结果最好,其次是α=2.76,变参数α较差;而从径向的收敛速度来看,变参数α收敛最快,α=2.76收敛较慢,α=z时本征能只有当对称基超过100时才呈现收敛趋势。结果表明,在超球谐展开方案下只有α=z的相关函数才能得到高精度的本征能量。

In consideration of the factor that the energy of the induced current on a scattering object excited by a plane wave with a Gaussian pulse almost all concentrates on a finite time and frequency-domain, by expanding the response in time with Laguerre function, a corresponding frequency-domain response is attained by using Fourier transform. According to the characters of Fourier transform, the low-frequency and high-frequency responses determine the late-time and early-time responses respectively. In this paper,...

In consideration of the factor that the energy of the induced current on a scattering object excited by a plane wave with a Gaussian pulse almost all concentrates on a finite time and frequency-domain, by expanding the response in time with Laguerre function, a corresponding frequency-domain response is attained by using Fourier transform. According to the characters of Fourier transform, the low-frequency and high-frequency responses determine the late-time and early-time responses respectively. In this paper, the early-time and low-frequency responses are generated through the use of a time-and-frequency hybrid method including MOT and MOM and they are mutually complementary and contain all the necessary information. So the whole response can be attained by simultaneous extrapolation in time and frequency domains. The electromagnetic scattering responses in the time and frequency domains of the ideal metal conductors are calculated and analyzed by using this method.

考虑到散射体在高斯脉冲平面波激励下感应电流的能量几乎全部集中在有限时间和频率的范围内这一因素,将时域响应用Laguerre函数展开,并由傅里叶变换,可得到相应的频域响应。采用时间步进法(MOT)和矩量法(MOM)分别得到早时和低频响应,由早时响应和低频响应信息的互补关系,联合外推得到整个时、频响应。用本方法分析计算了理想金属导线的时、频域电磁散射响应,结果表明了该方法与频域MOM、时域MOT的精确数值解非常接近。

 
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