Squeezed states in the quaternionic setting

Abstract

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 proper ties 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 canoni cal 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 pre vents 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.