The effective-mass Hamiltonian for abrupt heterostructures

Abstract
The effective-mass Hamiltonian H=1/2malpha pmbeta pmalpha +Vc+ upsilon for non-homogeneous semiconductors is studied. Here m is the position-dependent effective mass, 2 alpha + beta =-1. Vc 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,.