Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that pure squeezed states, which are obtained by the sole action of the squeeze operator on the vacuum state, can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also demonstrate that squeezed states, which are obtained by the action of the squeeze operator on canonical coherent states, in other words they are obtained by the action of the displacement operator followed by the action of the squeeze operator on the vacuum state, can be defined on the same Hilbert space, but the non-commutativity of quaternions prevents us in getting the desired results. However, we will show that if one considers the quaternionic slice wise approach, then the desired properties can be obtained for quaternionic squeezed states.

中文翻译：

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四元数环境中的压缩态

使用定义在右四元数希尔伯特空间上的左乘法，我们将证明通过挤压算子对真空状态的唯一作用获得的纯压缩状态可以在右四元数希尔伯特空间上定义为具有所有所需的属性. 此外，我们还将证明通过挤压算子对规范相干态的作用获得的挤压态，换句话说，它们是通过位移算子的作用和挤压算子对真空状态的作用获得的, 可以在同一个 Hilbert 空间上定义，但是四元数的非对易性阻止我们获得所需的结果。然而，我们将证明，如果考虑四元数切片明智的方法，