On the boundary conditions for envelope-function approaches for heterostructures

It is shown that integration of the set of differential equations that describes semiconductor heterostructures within the envelope-function approach gives the proper boundary conditions for the envelope functions at abrupt interfaces. These boundary conditions are correct in the sense that they ensure the continuity of the (cell-averages of the) particle density and the probability current density. Proper symmetrization rules for the effective Hamiltonian can be inferred from the requirement to conserve the probability current density.