This question can trace back to: why there’s band in crystal? In Neamen’s book, he has an interesting answer which I’ll quote here:
Figure 3.1a shows the radial probability density function for the lowest electron energy state of the single, noninteracting hydrogen atom, and Figure 3.1b shows the same probability curves for two atoms that are in close proximity to each other. The wave functions of the electrons of the two atoms overlap, which means that the two electrons will interact. This interaction or perturbation results in the discrete quantized
Neamen, P59
energy level splitting into two discrete energy levels, schematically shown in Figure 3.1c . The splitting of the discrete state into two states is consistent with the Pauli exclusion principle.
A simple analogy of the splitting of energy levels by interacting particles is the following. Two identical race cars and drivers are far apart on a race track. There is no interaction between the cars, so they both must provide the same power to achieve a given speed. However, if one car pulls up close behind the other car, there is an interaction called draft. The second car will be pulled to an extent by the lead car. The lead car will therefore require more power to achieve the same speed since it is pulling the second car, and the second car will require less power since it is being