Matching Conditions in Effective-Mass Theory
arXiv:1108.1224
Abstract
It has been shown that the traditional matching of wavefunctions between regions of different effective mass (matching ψ and (1/m*)\partialψ/\partialx) is not correct, but that one should match (1/\surdm*)ψ and (1/\surdm*)\partialψ/\partialx. It has not been clear how serious is the error in using the traditional formula. We apply the two sets of conditions to a simple, but rather general, example and find that the traditional matching is not even qualitatively correct.
2 figures, brief MS