# Stretching potential engineering

## TL;DR

This paper extends the concept of wavelength stretching from electromagnetic waves to massive particles, providing conditions for stable, flat wave-function regions in quantum systems and demonstrating applications in 1D and 2D models.

## Contribution

It introduces a general framework for wavelength stretching in quantum particles, identifying conditions for stable flat wave-function regions, which was not previously established.

## Key findings

- Derived necessary and sufficient conditions for stable flat wave-functions
- Applied the framework to well-known potential profiles
- Extended the analysis to two-dimensional quantum models

## Abstract

As the possibility to decouple temporal and spatial variations of the electromagnetic field, leading to a wavelength stretching, has been recognized to be of paramount importance for practical applications, we generalize the idea of stretchability from the framework of electromagnetic waves to massive particles. A necessary and sufficient condition which allows one to identify energetically stable configuration of a 1D quantum particle characterized by arbitrary large spatial regions where the associated wave-function exhibit a flat, non-zero profile is presented, together with examples on well-known and widely used potential profiles and an application to 2D models.