标题： 复数与四元数力学之间的奇数维变换 显示英文标题

标题： Odd Dimensional Translation between Complex and Quaternionic Mechanics

摘要： 我们通过复几何完成了标准复量子力学（CQM）与四元数量子力学（QQM）之间翻译规则的补充。 特别是我们描述了如何将 ($2n$+$1$)-维复矩阵简化为{\em 重叠}($n$+$1$)-维四元数矩阵，其中包含广义四元数元素。 这一步解决了在四元数QM中纯复矩阵群约简时的一个未解难题，并避免了{\em 异常}本征态。 作为结果，我们提供了从CQM到QQM以及反之更完整的翻译。 显示英文摘要

摘要： We complete the rules of translation between standard complex quantum mechanics (CQM) and quaternionic quantum mechanics (QQM) with a complex geometry. In particular we describe how to reduce ($2n$+$1$)-dimensional complex matrices to {\em overlapping\/} ($n$+$1$)-dimensional quaternionic matrices with generalized quaternionic elements. This step resolves an outstanding difficulty with reduction of purely complex matrix groups within quaternionic QM and avoids {\em anomalous} eigenstates. As a result we present a more complete translation from CQM to QQM and viceversa.