实线性四元数算子
Real linear quaternionic operators
摘要：
在最近的一篇论文[J.Math.Phys. vol 42，2236-2265（2001）]中，我们讨论了量子力学四元数公式中的微分算子。特别地，我们提出了一种求解四元数和复二阶常系数线性微分方程的实用方法。本文将我们的讨论推广到实线性四元数微分方程。分解方法是基于与实线性微分算子相关的四元数矩阵的若尔当典范形。
英文摘要：
In a recent paper [J.Math.Phys. vol42, 2236-2265 (2001)], we discussed differential operators within a quaternionic formulation of quantum mechanics. In particular, we proposed a practical method to solve quaternionic and complex linear second order differential equations with constant coefficients. In this paper, we extend our discussion to real linear quaternionic differential equations. The method of resolution is based on the Jordan canonical form of quaternionic matrices associoated to real linear differential operators.
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