Quaternionic eigenvalue problem

被引：44
作者：
De Leo, S
Scolarici, G
Solombrino, L
机构：
[1] Univ Estadual Campinas, Dept Appl Math, BR-13083970 Campinas, SP, Brazil
[2] Univ Lecce, Dept Phys, I-73100 Lecce, Italy
[3] Ist Nazl Fis Nucl, Sez Lecce, I-73100 Lecce, Italy
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2002年 / 43卷 / 11期
关键词：
D O I：
10.1063/1.1511789
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We discuss the (right) eigenvalue equation for H, C and R linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows us to translate the quaternionic problem into an equivalent real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics. (C) 2002 American Institute of Physics.
引用
收藏
页码：5815 / 5829
页数：15
相关论文
共 19 条
[1]  
Brenner J.L., 1951, PAC J MATH, V1, P329
[2]  
De Leo S, 2000, J PHYS A-MATH GEN, V33, P2971, DOI 10.1088/0305-4470/33/15/306
[3]   Quaternionic differential operators [J].
De Leo, S ;
Ducati, G .
JOURNAL OF MATHEMATICAL PHYSICS, 2001, 42 (05) :2236-2265
[4]   Quaternionic Lorentz group and Dirac equation [J].
De Leo, S .
FOUNDATIONS OF PHYSICS LETTERS, 2001, 14 (01) :37-50
[5]   Octonionic representations of GL(8,R) and GL(4,C) [J].
DeLeo, S ;
AbdelKhalek, K .
JOURNAL OF MATHEMATICAL PHYSICS, 1997, 38 (02) :582-598
[6]   Finding octonionic eigenvectors using Mathematica [J].
Dray, T ;
Manogue, CA .
COMPUTER PHYSICS COMMUNICATIONS, 1998, 115 (2-3) :536-547
[7]  
Dray T., 1998, Adv. Appl. Clifford Algebr, V8, P341, DOI [10.1007/BF03043104, DOI 10.1007/BF03043104]
[8]   QUATERNION QUANTUM-MECHANICS - 2ND QUANTIZATION AND GAUGE-FIELDS [J].
HORWITZ, LP ;
BIEDENHARN, LC .
ANNALS OF PHYSICS, 1984, 157 (02) :432-488
[9]   On two questions about quaternion matrices [J].
Huang, LP .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 318 (1-3) :79-86
[10]   On left eigenvalues of a quaternionic matrix [J].
Huang, LP ;
So, WS .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 323 (1-3) :105-116
12