  We investigate a quantum well that consists of a thin topological insulator
sandwiched between two trivial insulators. More specifically, we consider
smooth interfaces between these different types of materials such that the
interfaces host not only the chiral interface states, whose existence is
dictated by the bulk-edge correspondence, but also massive Volkov-Pankratov
states. We investigate possible hybridization between these interface states as
a function of the width of the topological material and of the characteristic
interface size. Most saliently, we find a strong qualitative difference between
an extremely weak effect on the chiral interface states and a more common
hybridization of the massive Volkov-Pankratov states that can be easily
understood in terms of quantum tunneling in the framework of the model of a
(Dirac) quantum well we introduce here.
