Abstract
A necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in an infinite-dimensional (right) quaternionic Hilbert space is proven. According to such results we obtain (and briefly discuss) two alternative descriptions of a quantum optical physical system, in the realm of quaternionic quantum mechanics, while no alternative can exist in complex quantum mechanics.
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