# The effective potential of an M-matrix

@article{Filoche2021TheEP,
title={The effective potential of an M-matrix},
author={Marcel Filoche and Svitlana Mayboroda and Terence Tao},
journal={Journal of Mathematical Physics},
year={2021},
volume={62},
pages={041902}
}
• Published 5 January 2021
• Mathematics
• Journal of Mathematical Physics
In the presence of a confining potential V, the eigenfunctions of a continuous Schrodinger operator −Δ + V decay exponentially with the rate governed by the part of V, which is above the corresponding eigenvalue; this can be quantified by a method of Agmon. Analogous localization properties can also be established for the eigenvectors of a discrete Schrodinger matrix. This note shows, perhaps surprisingly, that one can replace a discrete Schrodinger matrix by any real symmetric Z-matrix and…
2 Citations

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