Continuous and discrete frames generated by the evolution flow of the Schr\"odinger equation

TL;DR

This paper introduces Schr"odingerlets, a new family of coherent states derived from the Schr"odinger equation, applicable in both continuous and discrete frameworks, expanding the understanding of quantum state representations.

Contribution

It defines Schr"odingerlets based on the Schr"odinger equation and invariant transformations, providing a novel approach to quantum state analysis in continuous and discrete settings.

Findings

Schr"odingerlets form a new class of coherent states.

The framework applies to both continuous and discrete quantum systems.

Potential applications in quantum information and signal analysis.

Abstract

We study a family of coherent states, called Schr\"odingerlets, both in the continuous and discrete setting. They are defined in terms of the Schr\"odinger equation of a free quantum particle and some of its invariant transformations.