The effective-mass Hamiltonian H= 1 / 2 m alpha pm beta pm alpha +V c + upsilon for non-homogeneous semiconductors is studied. Here m is the position-dependent effective mass, 2 alpha + beta =-1. V c is the position-dependent conduction band edge and upsilon is a localised potential. Through an exact model calculation the authors show that when effective-mass theory is applicable, alpha =0 and beta =-1,.
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Einevoll et al. (1988) studied this question.
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