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

@article{Shigehara1999GeneralizedOP, title={Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics}, author={Takaomi Shigehara and Hiroshi Mizoguchi and Taketoshi Mishima and Taksu Cheon}, journal={arXiv: Quantum Physics}, year={1999} }

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…

## One Citation

### Band Spectra of Kronig-Penney Model with Generalized Contact Interaction

- Physics
- 1999

The standard Kronig-Penney model with periodic $\delta$ potentials is extended to the cases with generalized contact interactions. The eigen equation which determines the dispersion relation for…

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