Finite-Dimensional Bicomplex Hilbert Spaces

被引：31

作者：

Lavoie, Raphael Gervais ^{[1
]}

Marchildon, Louis ^{[1
]}

Rochon, Dominic ^{[2
]}

机构：

[1] Univ Quebec, Dept Phys, Trois Rivieres, PQ G9A 5H7, Canada

[2] Univ Quebec, Dept Math & Informat, Trois Rivieres, PQ G9A 5H7, Canada

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2011年 / 21卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Bicomplex numbers; bicomplex quantum mechanics; generalized quantum mechanics; Hilbert spaces; bicomplex matrix; bicomplex linear algebra; generalized linear algebra;

D O I：

10.1007/s00006-010-0274-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including the spectral decomposition theorem. Applications to concepts relevant to quantum mechanics, like the evolution operator, are pointed out.

引用

页码：561 / 581

页数：21

共 12 条

[1]

Adler SL., 1995, QUATERNIONIC QUANTUM

[2]

BOURBAKI N, 1962, ELEMENTS MATH, V6

[3]

Conway J., 1990, COURSE FUNCTIONAL AN

[4]

Hartley B., 1970, RINGS MODULES LINEAR

[5]

Herget C.J., 1993, APPL ALGEBRA FUNCTIO

[6]

LAVOIE RG, NUOVO CIM B IN PRESS

[7]

Lipschutz S., 2008, Schaum's Outline of Linear Algebra

[8]

Marchildon L., 2002, Quantum Mechanics: From Basic Principles to Numerical Methods and Applications

[9]

Price GB., 1991, An Introduction to Multicomplex Spaces and Functions

[10] Bicomplex quantum mechanics: II. The Hilbert space [J].

Rochon, D. ;

Tremblay, S. .

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2006, 16 (02) :135-157

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