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k • p method in envelope function approximation

The k•p method is widely used to find the band structure and wave functions of heterostructures. The basic assumption in this approaches is similarity between the matrix elements in the Hamiltonian for the various A3B5 compounds. The wave function inside each layer of heterostructure is expanded on the periodic parts of the Bloch functions of edges:
where k0 is the point in the Brillouin zone around which the heterostructure states are built [1]. The summation over i runs over all considered edges and l runs over all layers in heterostructure. The periodic part of the Bloch functions are assumed to be the same in each layer:
Thus the heterostructure wave function is written as

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