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高等学校化学研究 ›› 2000, Vol. 16 ›› Issue (3): 213-217.

• Articles • 上一篇    下一篇

Exact Radial Solution of the Non-relativistic Schrödinger Equation for the Helium Atom with the Potential Harmonic Method

WANG Yi-xuan, BU Yu-xiang, LIU Cheng-bu   

  1. Faculty of Chemistry, Shandong University, Jinan 250100, P. R. China
  • 收稿日期:1999-09-06 出版日期:2000-08-24 发布日期:2011-10-22
  • 基金资助:

    Supported by the National Natural Science Foundation of China(No.29703003).

Exact Radial Solution of the Non-relativistic Schrödinger Equation for the Helium Atom with the Potential Harmonic Method

WANG Yi-xuan, BU Yu-xiang, LIU Cheng-bu   

  1. Faculty of Chemistry, Shandong University, Jinan 250100, P. R. China
  • Received:1999-09-06 Online:2000-08-24 Published:2011-10-22
  • Supported by:

    Supported by the National Natural Science Foundation of China(No.29703003).

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摘要： We proposed a simple potential harmonic(PH) scheme for calculating the non-relativistic radial correlation energies of atomic systems.The scheme was applied to the low-lying n1S(n=1,2) and n3S(n=2,3) states of the helium atom.The results exhibit a very stable convergence characterization in both the angular and radial directions with PH and generalized Laguerre functions(GLF) respectively,even though the method is non-variational one.The ninth significant figure of the non-relativistic radial energy(NRE) calculated for the ground state exactly agrees with that of the most accurate literature data from the modified configuration interaction method.The convergent NRE′s for the excited states 21S,23S and 33S with the similar accuracy were also obtained.

关键词: Potential harmonic, Radial limit, Schrö, dinger equation, Helium atom

Abstract: We proposed a simple potential harmonic(PH) scheme for calculating the non-relativistic radial correlation energies of atomic systems.The scheme was applied to the low-lying n1S(n=1,2) and n3S(n=2,3) states of the helium atom.The results exhibit a very stable convergence characterization in both the angular and radial directions with PH and generalized Laguerre functions(GLF) respectively,even though the method is non-variational one.The ninth significant figure of the non-relativistic radial energy(NRE) calculated for the ground state exactly agrees with that of the most accurate literature data from the modified configuration interaction method.The convergent NRE′s for the excited states 21S,23S and 33S with the similar accuracy were also obtained.

Key words: Potential harmonic, Radial limit, Schrö, dinger equation, Helium atom