 Why do multiple electrons occupy the same orbital if electrons repel each other?

That is, two electrons per atomic orbital, each with a different spin.

As shown at Schrödinger equation solution for the helium atom, they do repel each other, and that affects their measurable energy.

However, this energy is still lower than going up to the next orbital. TODO numbers.

Bibliography:

This changes however at higher orbitals, notably as approximately described by the aufbau principle.