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#### Abstract

Summary. This notebook solves the ground state for the helium atom computationally within the mean field approximation using four Gaussian functions as the basis set. Assuming the two-electron wavefunction to be the product of two like orbitals, the two-particle Schrodinger equation reduces to single particle one but the effective Hamiltonian depends on the orbital one is trying to find (to describe electron-electron repulsion within mean field). This equation can be solved iteratively using self-consistent field (SCF) approach.

The initial part of the notebook go over the initial step in the SCF calculation starting from a guess wave function. All steps are described in detail. The second part performs the iterative SCF calculation until convergence is achieved.

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Purdue University