Configuration of heterostructure and general relations

(a) The physical configuration under study (6) the Frenkel and Wannier-Mott excitons in nanostructure (from (13)). 

2D translational invariance of the system, we classify the excitons by their inplane wavevector k. Supposing that for some bands of Frenkel excitons in the OQW and Wannier-Mott excitons in the IQW the energy separation is much less than the distance to other exciton bands we take into account only the hybridization between these two bands. We choose as a basis set the pure Frenkel and Wannier states, i.e. the state (denoted by F,k)) when the OQW is excited, while the IQW is in its ground state, and vice versa (denoted by W, k)), their energies being Ep(k) and W(k). We seek the new hybrid states in the form 

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