High-quality thin films of the topological insulator (Bi0.4Sb0.6)2Te3 have been deposited on SrTiO3 (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 (Bi0.4Sb0.6)2Te3 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.