Weakly coupled states on branching graphs

Pavel Exner

TBD mathscidoc:1910.43044

Letters in Mathematical Physics, 38, (3), 313-320, 1996.11
We consider a Schrdinger particle on a graph consisting of <i>N</i> links joined at a single point. Each link supports a real locally integrable potential <i>V</i> <sub> <i>j</i> </sub>; the self-adjointness is ensured by the type boundary condition at the vertex. If all the links are semi-infinite and ideally coupled, the potential decays as <i>x</i> <sup>1</sup> along each of them, is nonrepulsive in the mean and weak enough, the corresponding Schrdinger operator has a single negative eigenvalue; we find its asymptotic behavior. We also derive a bound on the number of bound states and explain how the coupling constant may be interpreted in terms of a family of squeezed potentials.
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  title={Weakly coupled states on branching graphs},
  author={Pavel Exner},
  booktitle={Letters in Mathematical Physics},
Pavel Exner. Weakly coupled states on branching graphs. 1996. Vol. 38. In Letters in Mathematical Physics. pp.313-320. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020122901313664573.
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