In this paper, an analytical energy band easy to calculate for GaAs, AlAs and AlGaAs is proposed. The transfer eigenvalue and energy effective mass are obtained by asing the LCAO transfer matrix model. By studing the transfer eigenrunction for two energy valleys, the transformation between different energy valleys is derived, from which new concepts about symmetry transformer and symmetry filter are suggested. Using the energy effective masses and the transformation coefficients between energy valleys at the interface, we derive the equations of envelope function and their boundary conditions for this single band-double valley model. Applying this theory to GaAs/AlGaAs/AlAs system, the confined energy level and wavefunc-tion are calculated. Finally, the significance of this generalized effective mass theory is discussed.
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