Continuum limit of resonances for discrete Schrödinger operators

What is it about?

We prove that complex resonances for discrete Schr\"odinger operators converge to those of continuous Schr\"odinger operators in the continuum limit. The proof employs the complex distortion in the Fourier space. We also construct approximate models for Schr\"odinger operators with singular potentials such as Coulomb potentials, and discuss the continuum limit of discrete eigenvalues and resonances.

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Photo by Yury Manulenko on Unsplash

Photo by Yury Manulenko on Unsplash