The octonionic eigenvalue problem

Abstract

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.

21 pages

References in corpus (3)

• Quaternionic potentials in non-relativistic quantum mechanics
• Quaternionic eigenvalue problem
• Solving simple quaternionic differential equations

Cited by in corpus (10)

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• Two incompatible types of invariants in the octonion spaces
• Gauge fields and four interactions in the trigintaduonion spaces
• Eight Equilibrium and continuity equations within the material media
• Frequencies of astrophysical jets and gravitational strengths in the octonion spaces
• Basic postulates of some coordinate transformations within material media
• Some field equations with composite operators in octonion spaces