For the purposes of the present discussion, we will assume that we possess a hermitian effective Hamiltonian which is valid throughout the structure, including any interval containing an abrupt heterointerface. The issues thus presumed to have been resolved have traditionally been posed as the definition of matching conditions for the mesoscopic wavefunction. These matching conditions are frequently ``derived'' from the continuity of J [2,3,4], but this condition is not sufficient to uniquely determine them [5]. The Hamiltonian and the matching conditions are equivalent pieces of information, in the sense that either one may be derived from the other. In contrast, the continuity of J follows solely from the hermiticity of H [6].
For the sake of simplicity, only the current density in one dimension will be considered. Extension to three-dimensional structures is in all cases straightforward, if somewhat tedious.