Reasoning behind the box shape

[sofiarips]

Maybe I am taking this too literally, but why would the electron be stuck near an atom in a box shape? Wouldn't a sphere or a wave-like sphere be more accurate? Or is this just an oversimplification to express that the electron is bound?

[Olivia Nokes 1H]

The orbitals and the box shape are completely theoretical. Electrons do not actually travel in these exact shapes; these shapes are more of a mathematical approach of thinking which area the electron could be found. Do not take the shapes literally, but think of it in terms of the area the electron is likely to be.

[Chem_Mod]

It's just a toy model. Basically, there are lots of models in quantum mechanics, because we very quickly move out of the realm where we can solve things analytically. The particle in a box, in particular, is one of the easiest models when learning quantum mechanics because there are solutions for the energies and wave functions. As we move to more realistic systems, for example, the hydrogen atom, it quickly gets more complex. In addition, while it might not be representative of most systems, there actually materials or systems that behave similarly to these "simple systems".