INFINITE-DIMENSIONAL BICOMPLEX HILBERT SPACES

被引：0

作者：

Lavoie, Raphael Gervais ^{[1
]}

Marchildon, Louis ^{[1
]}

Rochon, Dominic ^{[2
]}

机构：

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

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

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2010年 / 1卷 / 02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; Hilbert spaces; Banach algebras; bicomplex linear algebra;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex Hilbert space. Properties of such spaces are obtained through properties of several of their subsets which have the structure of genuine Hilbert spaces. In particular, we derive the Riesz representation theorem for bicomplex continuous linear functionals and a general version of the bicomplex Schwarz inequality. Applications to concepts relevant to quantum mechanics, specifically the bicomplex analogue of the quantum harmonic oscillator, are pointed out.

引用

页码：75 / 91

页数：17

共 14 条

[1]

Adler SL., 1995, QUATERNIONIC QUANTUM

[2]

Bourbaki N., 1962, ELEMENTS MATH

[3]

Conway J. B., 1990, COURSE FUNCTIONAL AN

[4]

Hansen V.L., 2006, FUNCTIONAL ANAL ENT

[5]

Herget C.J., 1993, APPL ALGEBRA FUNCTIO

[6] The bicomplex quantum harmonic oscillator [J].

Lavoie, R. Gervais ;

Marchildon, L. ;

Rochon, D. .

NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-BASIC TOPICS IN PHYSICS, 2010, 125 (10) :1173-1192

[7]

Lavoie R. Gervais, ADV APPL CL IN PRESS

[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

← 1 2 →