Electron states in two coupled quantum wells—A strong coupling-of-modes approach

In this paper, coupled-mode equations for two strongly coupled quantum wells are derived via two methods: (i) a ‘‘reciprocity’’ formulation similar to the reciprocity theorem in electromagnetics, and (ii) a variational formulation. It is shown that both formulations give the same coupled-mode equations. Numerical results for the electron energy levels and wave functions for two coupled asymmetric or symmetric quantum wells are presented, using both the strong coupling-of-modes theory and the conventional weak coupling-of-modes theory, and are compared with those of the exact calculations. The two-coupled-quantum-wells model is useful in the study of electron transport in superlattice via hopping or tunneling.