# 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} }

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

Applications of the landscape function for Schr\"odinger operators with singular potentials and irregular magnetic fields

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We resolve both a conjecture and a problem of Z. Shen from the 90’s regarding non-asymptotic bounds on the eigenvalue counting function of the magnetic Schrödinger operator La,V = −(∇ − ia) + V with…

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