  High quality thin films of the topological insulator
(Bi$_{0.4}$Sb$_{0.6}$)$_2$Te$_3$ have been deposited on SrTiO$_3$ (111) by
molecular beam epitaxy. Their electronic structure was investigated by in situ
angle-resolved photoemission spectroscopy and in situ scanning tunneling
spectroscopy. The experimental results reveal striking similarities with
relativistic ab-initio tight binding calculations. We find that ultrathin slabs
of the three-dimensional topological insulator (Bi$_{0.4}$Sb$_{0.6}$)$_2$Te$_3$
display topological surface states, surface states with large weight on the
outermost Te atomic layer, and dispersive bulk energy levels that are
quantized. We observe that the bandwidth of the bulk levels is strongly
reduced. These bunched bulk states as well as the surface states give rise to
strong peaks in the local density of states.
