Exact Radial Solution of the Non-relativistic Schr?dinger Equation for the Helium Atom with the Pote

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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.
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