Alternative Descriptions in Quaternionic Quantum Mechanics

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. Work supported in part by PRIN ”Sintesi”. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] 1 PACS: 03.65.-w, 03.65.Fd.