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Further Study on the Analytical Solution of Schr dinger Equation of a Hydrogen-Like Atom
Received date: 2001-04-16
Revised date: 2001-07-02
Online published: 2002-03-18
Based on the previous works, the Schrdinger equation of the hydrogen-like atom is analytically solved further. Three sets of analytical solutions are obtained if the factor r~ -nis not neglected. The first solution is the same as the traditional radial wave function, the second diverges, and the last one is quite different from the traditional solution. On the consideration of the finite size of the nuclear, the third wave function does not diverge when r approaches to zero. Its radial wave function has the following characteristics: (1) the angular-momentum quantum number l must be greater than the principal quantum number n; (2) l must not be 0 or 1; (3) the electron-cloud distribution differs from the traditional one; (4) the electron is closer to the nuclear than that in traditional results. On the other hand, the validity of solutions needs to be verified experimentally.
Key words： hydrogen atom; hydrogen-like atom; Schringer equation
ZHANG Zhong-Liang , ZHANG Wu-Shou . Further Study on the Analytical Solution of Schr dinger Equation of a Hydrogen-Like Atom[J]. Journal of University of Chinese Academy of Sciences, 2002 , 19(2) : 186 -191 . DOI: 10.7523/j.issn.2095-6134.2002.2.016
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