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.
