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Continuum limit of resonances for discrete Schrödinger operators

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This research shows resonances in discrete models converge to those in continuous models, implying new methods for computing them.

Resonances from discrete Schrödinger operators converge to those from continuous models in the continuum limit.
The method employs norm resolvent convergence and complex distortion techniques, confirming effective resonance computation.
Using exterior dilation analytic functions, we construct approximate discrete operators for Schrödinger operators with singular potentials.
The findings enhance our understanding of resonance behavior in quantum mechanics, potentially improving calculations in complex systems.

Kameoka et al. (2025) studied this question.

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