Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics

摘要

We first give the solution for the local approximation of a four parameterfamily of generalized one-dimensional point interactions within the frameworkof non-relativistic model with three neighboring $\delta$ functions. We alsodiscuss the problem within relativistic (Dirac) framework and give the solutionfor a three parameter family. It gives a physical interpretation for so-called$\epsilon$ potential. It will be also shown that the scattering properties athigh energy substantially differ between non-relativistic and relativisticcases.