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无限求和
相关语句
  相似匹配句对
     The Sum of p-series
     p级数的求和
短句来源
     Siemens AG Information & Communication Networks
     网络无限
     To the Sum of Series
     级数求和
短句来源
     Science:Its Infinitude and Boundary
     科学的无限有界性
短句来源
     new method of calculating summation of series is constructed by using a set of suitable wave functions in an infinite square potential well of one dimension.
     利用一维无限深方势阱中一套适当的波函数,建立了一种新的级数求和方法。
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In this paper, an entire new approach for quantum mechanics calculation, the non-degenerate ground state steepest descent perturbation theory (SDPT) suggested by Cioslowski is developed and extended for dealing with degenerate ground state problem. Using sysmme-try adapted trial wave ket, the SDPT iteration for different sublevel is independent from each other and improves its eigen energy and wave function step by step. Therefore, the steepest descent perturbation theory can be used to calculate the low symmetry...

In this paper, an entire new approach for quantum mechanics calculation, the non-degenerate ground state steepest descent perturbation theory (SDPT) suggested by Cioslowski is developed and extended for dealing with degenerate ground state problem. Using sysmme-try adapted trial wave ket, the SDPT iteration for different sublevel is independent from each other and improves its eigen energy and wave function step by step. Therefore, the steepest descent perturbation theory can be used to calculate the low symmetry splitting of degenerate ground state and the correlation energy to arbitrary precison. Unlike other perturbation theory, this does not require either infinite summation overlstates or the solution of a set of differential equations, it could be expected wide adaptability in the calculation of energy level perturbation splitting of atoms, molecules and orther many body quantum system.

本文证明,Cioslowski所引入的一个全新的量子力学计算方案,非简并基态最陡下降微扰理论,通过按对称性选择合适的零级试探波函数后,可以处理简并基态的微扰分裂问题由于最陡下降微扰理论既避免了通常的其他微扰理论需要对各个基矢量无限求和的或求解一组微分方程的缺陷,又具有逐步迭代改善计算结果的优点,本文引进的计算方案可望在原子分子及其他多粒子体系能级的微扰分裂计算中得到广泛应用。

The steepest descent perturbation theory is extended to the calculation of the energy and eigenfunction of the excited state of a quantum system. In case of the orthogonality of the trial function for the excited state to those for lower-energy state or ground state in the same symmetry class is preserved, the variational collapse to lower energy state can be avoided in this proposal. An iterative procedure is given for generating better eigenvalue and eigenfunction of the excited state without requiring an...

The steepest descent perturbation theory is extended to the calculation of the energy and eigenfunction of the excited state of a quantum system. In case of the orthogonality of the trial function for the excited state to those for lower-energy state or ground state in the same symmetry class is preserved, the variational collapse to lower energy state can be avoided in this proposal. An iterative procedure is given for generating better eigenvalue and eigenfunction of the excited state without requiring an infinite summation over reference states as in conventional perturbation theory. This new perturbation method can be applied to calculate the excitation energy and wave function of excited states for any many-body quantum system to a high degree of accuracy without so much computational effort as in conventional method.

本文发展了量子激发态能量与波函数的最陡下降微扰理论计算方法,该方法避免了普通微扰理论所需要的对于参考态的无限求和困难,并能通过逐步迭代计算逼近于体系精确的本征函数和本征值。只要保持激发态试探波函数正交于其对称性相同的低激发态或基态的波函数,避免计算过程中的变分坍陷,本文的方法能用于求精确的激发态能量和波函数。

The main purpose of this paper uses two common combination identities and elementary method to study the combination numbers.Four orderliness combinatorial identities of combination numbers reciprocal are obtained.Infinity summing formula and simple combination formula are deduced.

利用常见的两个组合恒等式以及初等方法,得出了4个有规律的组合数倒数的组合恒等式,以及两个重要推论,即无限求和公式和简单组合公式。

 
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