# A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators

@article{Kaminaga2019ASC,
title={A Self-adjointness Criterion for the Schr{\"o}dinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators},
author={Masahiro Kaminaga and Takuya Mine and Fumihiko Nakano},
journal={Annales Henri Poincar{\'e}},
year={2019},
volume={21},
pages={405-435}
}
• Published 1 June 2019
• Mathematics
• Annales Henri Poincaré
We prove the Schrödinger operator with infinitely many point interactions in $$\mathbb {R}^d$$ R d $$(d=1,2,3)$$ ( d = 1 , 2 , 3 ) is self-adjoint if the support $$\Gamma$$ Γ of the interactions is decomposed into infinitely many bounded subsets $$\{\Gamma _j\}_j$$ { Γ j } j such that $$\inf _{j\not =k}\mathop {\mathrm{dist}}\nolimits (\Gamma _j,\Gamma _k)>0$$ inf j ≠ k dist ( Γ j , Γ k ) > 0 . Using this fact, we prove the self-adjointness of the Schrödinger operator with point interactions…
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