# Squeezed states in the quaternionic setting

## TL;DR

This paper explores the definition and properties of squeezed states within quaternionic Hilbert spaces, demonstrating how noncommutativity affects their construction and proposing a slice-wise approach to overcome these challenges.

## Contribution

It introduces a method to define pure quaternionic squeezed states with desired properties using a slice-wise approach, addressing noncommutativity issues.

## Key findings

- Pure squeezed states can be defined with desired properties on quaternionic Hilbert spaces.
- Noncommutativity of quaternions complicates the construction of squeezed states.
- Slice-wise approach enables the realization of quaternionic squeezed states with proper properties.

## Abstract

Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that pure squeezed states can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also demonstrate squeezed states can be defined on the same Hilbert space, but the noncommutativity of quaternions prevent us in getting the desired results. However, we will show that if once considers the quaternionic slice wise approach, then the desired properties can be obtained for quaternionic squeezed states.