{c}

No closed form solution, but good approximation that can be calculated by hand with the <Hartree-Fock method>, see <hartree-Fock method for the helium atom>.

Bibliography:
* https://www.quora.com/Why-do-electrons-not-repel-each-other-on-their-orbits
* https://physics.stackexchange.com/questions/224108/what-does-an-orbital-mean-in-atoms-with-multiple-electrons-what-do-the-orbitals

\Video[https://www.youtube.com/watch?v=tcfNNGGjS2o]
{title=Quantum Chemistry 9.2 - Helium Atom Energy Approximations by TMP Chem (2016)}
{description=Video gives the actual numerical value of various methods, second order <perturbation theory> being very close. But it the says that in the following videos will only do <Hartree-Fock method>[Hartree-Fock method].}


Schrödinger equation solution for the helium atom