Alternative Descriptions in Quaternionic Quantum Mechanics

Abstract

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.

16 pages

References in corpus (4)

• On the pseudo-Hermitian nondiagonalizable Hamiltonians
• Quaternionic eigenvalue problem
• C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians
• Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries

Cited by in corpus (5)

• Non-anti-hermitian quaternionic quantum mechanics
• Quaternions in mathematical physics (1): Alphabetical bibliography
• Complex Projection of Quasianti-Hermitian Quaternionic Hamiltonian Dynamics
• Quasistationary quaternionic Hamiltonians and complex stochastic maps
• Alternative Algebraic Structures from Bi-Hamiltonian Quantum Systems