Quaternionic eigenvalue problem

Abstract

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.

13 pages, AMS-TeX

References in corpus (5)

• Right eigenvalue equation in quaternionic quantum mechanics
• Quaternionic potentials in non-relativistic quantum mechanics
• Quaternionic differential operators
• Octonionic Representations of GL(8,R) and GL(4,C)
• Finding Octonionic Eigenvectors Using Mathematica

Cited by in corpus (8)

• Solving simple quaternionic differential equations
• Delay Time in Quaternionic Quantum Mechanics
• The octonionic eigenvalue problem
• A Closed Formula for the Barrier Transmission Coefficient in Quaternionic Quantum mechanics
• Alternative Descriptions in Quaternionic Quantum Mechanics
• An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry
• On compact affine quaternionic curves and surfaces
• The Snell law for quaternionic potentials