Finite Approximations of Physical Models over Local Fields

TL;DR

This paper demonstrates that Schr"odinger operators over local fields can be strongly approximated by finite models, providing new numerical insights into such physical systems over non-Archimedean fields.

Contribution

It introduces a method for finite approximation of Schr"odinger operators over local fields, bridging infinite models and computationally feasible finite systems.

Findings

Strong approximation results for Schr"odinger operators over local fields

Numerical experiments illustrating the approximation quality

Potential applications in computational physics over non-Archimedean fields

Abstract

We show that the Schr\"odinger operator associated with a physical system over a local field can be approximated in a very strong sense by finite Schr\"odinger operators. Some striking numerical results are included at the end of the article.