A result in atomic theory stating that the square of the total wave function for a full or half-full sub-shell (see atom) is spherically symmetric. It applies to all s-sub-shells, p-sub-shells with three or six electrons, d-sub-shells with five or ten electrons, and f-sub-shells with seven or fourteen electrons. The theorem determines which atoms are spherical. It was first stated and proved by the German astrophysicist Albrecht Unsöld in 1927, using properties of spherical harmonics. It can also be used with group theory.