A new class of solvable models in quantum mechanics describing point interactions on the line

The authors provide a detailed analysis of properties of the Schroedinger operator in L2(R). The model allows for an explicit calculation of spectral properties. Special emphasis is given to the periodic case where the spectrum and the density of states are explicitly computed. Also the spectrum for a half-crystal is given. Spectral consequences are studied when various defects and impurities are added to the periodic case. (author)