Document Type

Article

Publication Date

8-1-2021

Abstract

We investigate the spectrum of Schrödinger operators on finite regular metric trees through a relation to orthogonal polynomials that provides a graphical perspective. As the Robin vertex parameter tends to -∞, a narrow cluster of finitely many eigenvalues tends to -∞, while the eigenvalues above this cluster remain bounded from below. Certain “rogue” eigenvalues break away from this cluster and tend even faster toward -∞. The spectrum can be visualized as the intersection points of two objects in the plane—a spiral curve depending on the Schrödinger potential, and a set of curves depending on the branching factor, the diameter of the tree, and the Robin parameter.

Publication Source (Journal or Book title)

Annales Henri Poincare

First Page

2531

Last Page

2561

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