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Exact solutions of the Schrödinger equation for 1,3 S states of the atom with Fues–Kratzer‐type potential
Author(s) -
Yalçın Zeynel,
Aktaş Meti̇n,
Şi̇mşek Mehmet
Publication year - 2000
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(2000)76:5<618::aid-qua4>3.0.co;2-9
Subject(s) - laguerre polynomials , eigenvalues and eigenvectors , wave function , physics , mathematical physics , schrödinger equation , harmonics , quantum mechanics , electron , excited state , eigenfunction , type (biology) , ecology , biology , voltage
In this article exact solutions of a two‐electron Schrödinger equation for the Coulomb potential were extended to the Fues–Kratzer‐type potential: \documentclass{article}\pagestyle{empty}\begin{document}$(\hat{Z}(\Omega)/r)+(\hat{A}/r^{2})$\end{document} . The wave function Ψ( r ,Ω) is expanded into generalized Laguerre polynomials and hyperspherical harmonics. An analytical expression of two‐electron systems is given for matrix elements and accurate energy eigenvalues of the excited state of 1,3 S helium are calculated by using the hyperspherical harmonics method. The present results are compared with previous theoretical calculations and it is concluded that the convergence of energy eigenvalues is faster. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 618–625, 2000