Alternative descriptions in quaternionic quantum mechanics

A. Blasi, G. Scolarici, L. Solombrino
2005 Journal of Mathematical Physics  
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
more » ... , while no alternative can exist in complex quantum mechanics, and we discuss some differences between them.
doi:10.1063/1.1873040 fatcat:f2myyazo65ag5cqhom7v4cqqpu