GENERALIZED POINT INTERACTIONS IN ONE-DIMENSIONAL QUANTUM-MECHANICS

There is a four-parameter family of point interactions in one-dimensio nal quantum mechanics. They represent all possible self-adjoint extens ions of the kinetic energy operator. If time-reversal invariance is im posed, the number of parameters is reduced to three. One of these poin t interactions is the familiar delta function potential but the other generalized ones do not seem to be widely known. We present a pedestri an approach to this subject and comment on a recent controversy in the literature concerning the so-called delta' interaction. We emphasize that there is little resemblance between the delta' interaction and wh at its name suggests.