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Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that various classes of coherent states such as the canonical coherent states, pure squeezed states which are obtained by the sole action of the squeeze operator on the vacuum state, fermionic coherent states can be defined with all the desired properties on a right quaternionic Hilbert space. Furthermore, 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 squeeze operator followed by the action of the displacement operator on the vacuum state, can be defined on the same Hilbert space, but the noncommutativity of quaternions prevents us in getting the desired results.

Canonical, Squeezed and Fermionic Coherent States in a Right Quaternionic Hilbert Space with a Left Multiplication on It