Alternative descriptions in quaternionic quantum mechanics
Alberto Blasi, G. Scolarici, Luigi Solombrino
We characterize the quasianti-Hermitian quaternionic operators in quaternionic quantum mechanics 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.
arXiv:quant-ph/0407158•Journal of Mathematical Physics•Mar 21, 2005•11 citations