Transparency at the interface between two isospectral crystals

Reflection at an interface separating two different media is a rather universal phenomenon which arises because of wave mismatching at the interface. By means of supersymmetric quantum mechanics methods, it is shown that a fully transparent interface can be realized, connecting two isospectral but different one-dimensional crystals. An example of reflectionless interface is presented for the sinusoidal (Mathieu) crystal connected to a non-sinusoidal potential by a transparent domain wall.