6.B: Simplification of many-electron wave functions
Fortunately, there are major simplifications that allows us to write many-electron wave functions with acceptable accuracy. They arise from the fact that electrons are highly quantum mechanical in their behavior. Their wave functions are spread over relatively large areas. As a consequence, each electron in a many-electron atom doesn't see the sharp electrostatic repulsion of the other negatively charged electrons as if the other electrons were sitting in a fixed positions. Rather, it sees the other electrons spread out over the whole atom: electron Jello!
Each electron in a many-electron atom feels the electric field of the nucleus plus the smeared out charge cloud of the other electrons. This produces an environment that is not too different from the single electron in hydrogen. This has several consequences. Firstly, it means that each electron moves, to a first approximation, independently of the others. Secondly, it means that wave functions resembling the hydrogen atom eigenstates are a useful first approximations for the wave functions of electrons in many-electron atoms.
Returning to helium, the conclusions of the previous paragraph imply that the two electrons of helium move independently with wave functions that look similar to hydrogen atom wave functions. Since, the 1s state is the ground state of hydrogen, we expect that the ground state of helium resembles two electrons in 1s states. Therefore the helium wave function can be approximated well by a product of hydrogen wave functions for each of the two electrons.
When single-electron wave functions are used as part of a many-electron wave function, as they are in the above equation, those single-electron wave functions are called orbitals. A chemist would say that the two electrons of helium ``are in 1s orbitals''.