Energy-dependent point interactions in one dimension - Coutinho, FAB; Nogami, Y.; Tomio, L.; Toyama, F. M. (Iop Publishing Ltd, 2005)
We consider a new type of point interaction in one-dimensional quantum mechanics. It is characterized by a boundary condition at the origin that involves the second and/or higher order derivatives of the wavefunction. The interaction is effectively energy dependent. It leads to a unitary S-matrix for the transmission-reflection problem. The energy dependence of the interaction can be chosen such that any given unitary S-matrix (or the transmission and reflection coefficients) can be reproduced at all energies. Generalization of the results to coupled-channel cases is discussed.