  We characterize the quasianti-Hermitian quaternionic operators in QQM by
means of their spectra; moreover, we state 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 a infinite
dimensional (right) quaternionic Hilbert space. According to such results we
obtain 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, and we discuss some differences between them.
