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Some properties of the one-dimensional generalized point interactions (a torso)

Pavel Exner Harald Grosse

TBD mathscidoc:1910.43085

arXiv preprint math-ph/9910029, 1999.10
This text is a part of an unfinished project which deals with the generalized point interaction (GPI) in one dimension. We employ two natural parametrizations, which are known but have not attracted much attention, to express the resolvent of the GPI Hamiltonian as well as its spectral and scattering properties. It is also shown that the GPI yields one of the simplest models in which a non-trivial Berry phase is exhibited. Furthermore, the generalized Kronig-Penney model corresponding to the GPI is discussed. We show that there are three different types of the high-energy behaviour for the corresponding band spectrum.
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[ Download ] [ 2019-10-20 12:54:56 uploaded by Pavel_Exner ] [ 361 downloads ] [ 0 comments ] 
@inproceedings{pavel1999some,
  title={Some properties of the one-dimensional generalized point interactions (a torso)},
  author={Pavel Exner, and Harald Grosse},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125456725957614},
  booktitle={arXiv preprint math-ph/9910029},
  year={1999},
}
Pavel Exner, and Harald Grosse. Some properties of the one-dimensional generalized point interactions (a torso). 1999. In arXiv preprint math-ph/9910029. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125456725957614.
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