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 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.
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Acknowledgments
K. Thirulogasanthar would like to thank the, FQRNT, Fonds de la Recherche Nature et Technologies (Quebec, Canada) for partial financial support Under the grant number 2017-CO-201915. Part of this work was done while he was visiting the Politecnico di Milano to which he expresses his thanks for the hospitality. He also thanks the program Professori Visitatori GNSAGA, INDAM for the support during the period in which this paper was partially written. The authors thank Prof. I Sabadini for discussions. The authors would also like to thank the reviewer for his/her valuable comments.
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Thirulogasanthar, K., Muraleetharan, B. Squeezed States in the Quaternionic Setting. Math Phys Anal Geom 23, 8 (2020). https://doi.org/10.1007/s11040-020-9332-6
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DOI: https://doi.org/10.1007/s11040-020-9332-6