The interface between two one-dimensional crystals is studied with the use of the transfer matrix. This microscopic approach allows a study of the accuracy of the effective-mass approximation (EMA) and derivation of the boundary conditions (BC) for the envelope functions. These BC turn out to be very different from those adopted so far: they contain an additional microscopic parameter (independent of the effective masses) which characterizes the interface and may be as important as the band offset. It is shown that it is not possible to generalize the EMA to abrupt heterojunctions. When the band edges on two sides of the interface are of different types (as in GaAs/AlAs), the BC are unusual and can lead to the existence of interface states and also to a strong modification of the bound states in a single quantum well.