# How to understand orbitals in a unit cell?

I am doing a topology in condensed matter course and they begin with a sentence ( link here )

Actually, we can even solve the problem of an electron in an N site ring (triangle being 𝑁=3). The trick to doing this is a neat theorem called Bloch’s theorem. Bloch’s theorem is the key to understanding electrons in a crystal. The defining property of a crystal is that the atomic positions repeat in a periodic manner in space. We account for ALL the atoms in the crystal by first identifying a finite group of orbitals called the unit-cell.

As far as I learned, a unit cell consists of atoms, and by translating it we can recreate the whole lattice. As an orbital, I understand the solution of Schrodinger's equation. But I don't know how to understand or imagine the sentence

identifying a finite group of orbitals called the unit-cell.

Because I was thinking in my mind about some structures with points, balls meaning atoms, not orbitals.

• The point is that if there is a crystal lattice, with associated symmetries, the solutions to the electron wavefunctions will also have those associated symmetries, and spatially will be reflected by having a set of orbitals within a unit cell. Apr 20, 2023 at 15:05