On the Problem of the Exact Shape of Orbitals

To explain the inconsistency in the representation of the orbital in many textbooks, we considered the contour and polar representation of dz2 orbitals. Most introductory textbooks use the polar representation in their discussions, but the dz2 orbitals seems to be the most misrepresented orbital. In particular it is represented with a “lifesaver’’ middle section. We argue that this shape belongs to the contour representation and is inconsistent with the polar representation.