For a certain device (that can be used as a detector of optical radiation) we fabricate a coupled well structure, where electrons sitting inside GaAs...

For a certain device (that can be used as a detector of optical radiation) we fabricate a coupled well structure, where electrons sitting inside GaAs layers see the interface with AlGaAs layer as a potential barrier of height . Assume that the width of the GaAs wells is , while the width of the barrier is  the mass of electrons inside GaAs is mGaAs=0.067 , mass of AlGaAs=0.092 . where  is s the mass of the free electron.  

Now consider the system of two wells . Derive an equation for energies of the bound states in this system, applying boundary conditions at each interface (you will end up with 8 equations). But if you choose the origin of the coordinate system at the center of the AlGaAs barrier, you can use the symmetry arguments and consider odd and even solutions separately, which will reduce the number of equations to four for solutions of each parity. Find discrete energy levels using first graphing method,