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The two-electron atomic systems. S-states

Evgeny Z. Liverts
Organization: Hebrew University, Jerusalem
Department: Racah Institute of Physics
Nir Barnea
Organization: Hebrew University, Jerusalem
Department: Racah Institute of Physics
Journal / Anthology

Computer Physics Communications
Year: 2010
Volume: 181
Issue: 1
Page range: 206-212

A simple Mathematica program for computing the S-state energies and wave functions of twoelectron (helium-like) atoms (ions) is presented. The well-known method of projecting the Schrödinger equation onto the finite subspace of basis functions was applied. The basis functions are composed of the exponentials combined with integer powers of the simplest perimetric coordinates. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of results and computation time depend on the basis size. The precise energy values of 7–8 significant figures along with the corresponding wave functions can be computed on a single processor within a few minutes. The resultant wave functions have a simple analytical form consisting of elementary functions, that enables one to calculate the expectation values of arbitrary physical operators without any difficulties.