  Exact diagonalization is used to study the quantum states of vertically
coupled quantum dots in strong magnetic fields. We find a new sequence of
angular momentum magic numbers which are a consequence of the electron
correlation in the double dot. The new sequence occurs at low angular momenta
and changes into the single dot sequence at a critical angular momentum
determined by the strength of the inter-dot electron tunneling. We also propose
that the magic numbers can be investigated experimentally in vertically coupled
dots. Because of the generalized Kohn theorem, the far-infrared optical
absorption spectrum of a single dot is unaffected by correlation but the
theorem does not hold for two vertically coupled dots which have different
confining potentials. We show that the absorption energy of the double dot
should exhibit discontinuities at the magnetic fields where the total angular
momentum changes from one magic number to another.
