New analytically solvable models of relativistic point interactions (Q1103979)

Two new analytically solvable models of relativistic point interactions in one dimension (being natural extensions of the nonrelativistic \(\delta\), resp. \(\delta\) ', interactions) are considered. Their spectral properties in the case of finitely many point interactions as well as in the periodic case are fully analyzed. Moreover, we explicitly determine the spectrum in the case of independent, identically distributed random coupling constants and derive the analog of the \textit{D. S. Saxon} and \textit{R. A. Hutner} conjecture [Philos. Res. Rep. 4, 81 ff. (1949)] concerning gaps in the energy spectrum of such systems.