# Three-Parameter Variational Wavefunctions for the Helium Isoelectronic Series

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An optimized three-parameter variational wavefunction for the helium isoelectronic series , , , …, can give quite accurate values for the ground-state energies. This computation is based on a simplified version of Hylleraas' classic work on two-electron atoms [1]. The Schrödinger equation for a two-electron atom with nuclear charge can be written as

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Contributed by: S. M. Blinder (April 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The calculated optimal values are given in the following table.

Reference

[1] H. A. Bethe and E. E. Salpeter, *Quantum Mechanics of One- and Two-Electron Atoms*, Berlin: Springer–Verlag, 1957 pp. 146–154.

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