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

Physics – Quantum Physics

Scientific paper

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LaTeX 4 Pages, Talk to be presented at The 1999 International Symposium on Nonlinear Theory and Its Applications (NOLTA99) Hil

Scientific paper

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

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