Alternative Descriptions in Quaternionic Quantum Mechanics

Details Alternative Descriptions in Quaternionic Quantum Mechanics Alternative Descriptions in Quaternionic Quantum Mechanics

2004-07-20

arxiv.org/abs/quant-ph/0407158v1

Physics

Quantum Physics

16 pages

Scientific paper

10.1063/1.1873040

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.

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