Finite-Dimensional Bicomplex Hilbert Spaces

被引：0

作者：

Raphaël Gervais Lavoie

Louis Marchildon

Dominic Rochon

机构：

[1] Université du Québec à Trois-Rivières,Département de physique

[2] Université du Québec à Trois-Rivières,Département de mathématiques et d’informatique

来源：

Advances in Applied Clifford Algebras | 2011年 / 21卷

关键词：

16D10; 30G35; 46C05; 46C50; Bicomplex numbers; bicomplex quantum mechanics; generalized quantum mechanics; Hilbert spaces; bicomplex matrix; bicomplex linear algebra; generalized linear algebra;

D O I：

暂无

中图分类号：

学科分类号：

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：20

共 6 条

[1]

Rochon D.(2004)Bicomplex quantum mechanics: I. The generalized Schrödinger equation Adv. appl. Clifford alg. 14 231-248

[2]

Tremblay S.(2006)Bicomplex quantum mechanics: II. The Hilbert space Adv. appl. Clifford alg. 16 135-157

[3]

Rochon D.(2004)On algebraic properties of bicomplex and hyperbolic numbers Analele Universitatii Oradea, Fasc. Matematica 11 71-110

[4]

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