# Pseudomodes for Schroedinger operators with complex potentials

## TL;DR

This paper develops a method to construct pseudomodes for one-dimensional Schrödinger operators with complex potentials, including discontinuous ones, advancing the understanding of their spectral properties.

## Contribution

It introduces a non-semi-classical approach to construct pseudomodes for complex potentials, covering a broader class of potentials than previously possible.

## Key findings

- Constructed pseudomodes for large pseudoeigenvalues
- Achieved optimal conditions for a wide class of potentials
- Included discontinuous potentials in the analysis

## Abstract

For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including discontinuous ones.