Asymptotics of atomic ground states: The relation between the ground state of helium and the ground state of He+
- 1 June 1981
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (6) , 1299-1305
- https://doi.org/10.1063/1.525023
Abstract
The asymptotic behavior of ground states of two‐electron atoms is investigated. Suppose ψ(x1,x2) is the ground state of helium, ρ(x1) = Fψ2(x1,x2) dx2 the corresponding electron density, and Φ(x2) the ground state of He+. We show that in the L2(dx2)‐sense, lim‖x1‖→∞ ψ(x1,x2)[ρ(x1)]−1/2 = Φ(x2), and that ψ[ρ(x1)]−1/2 solves for large ‖x1‖ the Schrödinger equation for He+ in the quadratic form sense. The rate of convergence of these limits is also discussed.Keywords
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