An isoperimetric problem for point interactions

Pavel Exner

TBD mathscidoc:1910.43133

Journal of Physics A: Mathematical and General, 38, (22), 4795, 2005.5
We consider a Hamiltonian with N point interactions in {\bb R}^ d,\: d= 2, 3, all with the same coupling constant, placed at vertices of an equilateral polygon {\cal P} _N. It is shown that the ground-state energy is locally maximized by a regular polygon. The question whether the maximum is global is reduced to an interesting geometric problem.
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@inproceedings{pavel2005an,
  title={An isoperimetric problem for point interactions},
  author={Pavel Exner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130946391683662},
  booktitle={Journal of Physics A: Mathematical and General},
  volume={38},
  number={22},
  pages={4795},
  year={2005},
}
Pavel Exner. An isoperimetric problem for point interactions. 2005. Vol. 38. In Journal of Physics A: Mathematical and General. pp.4795. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130946391683662.
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