Connection rules versus differential equations for envelope functions in abrupt heterostructures

The controversial question of whether envelope functions are continuous or discontinuous at an abrupt heterojunction is addressed by developing a systematic procedure for obtaining interface connection rules from differential equations. The results show that even though modern envelope-function theories are smooth and continuous, their associated connection rules are discontinuous, in agreement with traditional concepts. This resolves the dispute in favor of both sides, by showing that the two views are physically equivalent.