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

T. Shigehara·H. Mizoguchi·T. Mishima·Taksu Cheon
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Abstract

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 $δ$ 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 $ε$ 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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T. Shigehara, H. Mizoguchi, T. Mishima, Taksu Cheon. 1999-11-13. Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics. https://arxiv.org/abs/quant-ph/9911059

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