If the bound states are such that the evanescent components in the adjascent wells do not overlap appreciably, then the quantum wells are essentially uncoupled and such systems are called Multiple Quantum Wells (MQW’s). The levels are N-fold degenerate for N number of wells. If the overlap is appreciable, then the N-degenerate states are split. For N = 2 (see Fig 2.5), it is like in H-molecule, states splitting into singlet and triplet molecular states. If N is large, the problem is similar to the Kronig-Penney model, and each N-fold degenerate state is split into bands.

In such a case,

where L_s is the period of the super-lattice. In such a situation one has to resort to numerical work, unless N is very large and periodic boundary condition used.

However, N is always finite, and this means that there will be surface states appearing in the band gaps as well.