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arXiv · 1906.00206

A self-adjointness criterion for the Schr\"odinger operator with infinitely many point interactions and its application to random operators

Masahiro Kaminaga·Takuya Mine·Fumihiko Nakano
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Abstract

We prove the Schr\"odinger operator with infinitely many point interactions in $\mathbb{R}^d$ $(d=1,2,3)$ is self-adjoint if the support of the interactions is decomposed into uniformly discrete clusters. Using this fact, we prove the self-adjointness of the Schr\"odinger operator with point interactions on a random perturbation of a lattice or on the Poisson configuration. We also determine the spectrum of the Schr\"odinger operators with random point interactions of Poisson--Anderson type.

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Masahiro Kaminaga, Takuya Mine, Fumihiko Nakano. 2019-06-01. A self-adjointness criterion for the Schr\"odinger operator with infinitely many point interactions and its application to random operators. https://doi.org/10.1007/s00023-019-00869-1

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