Existence of orbitals Do orbitals exist even when they are not occupied?

For example: $\ce{Cr^{+3}}$ has the configuration $\ce{[Ar]}\mathrm{3d^3}$ with the other two $\mathrm{3d}$ orbitals empty. We know the  other two orbitals exist, since the metal "uses its empty $\mathrm{d}$ orbitals" to form complexes.

But, for $\ce{Na+}$ with configuration $\ce{[Ne]}$, do the $\mathrm{3s,3p}$ and $\mathrm{3d}$ orbitals exist  too?
Do orbitals exist even when they are occupied? Orbitals are mathematical constructs and as such they exist in a mathematical sense regardless of whether they are occupied or not. Whether you can actually say that orbitals exist in reality is a bit dubious. They certainly provide a good description of the observed electron density and behaviour of atoms but they are still only a model. Like everything in science, we develop a model to describe what we observe but that model is not perfect and does not necessarily represent what actually exists. Particularly on a quantum scale, the notion of well defined objects that exist in space starts to become a bit fuzzy.