The bicomplex quantum harmonic oscillator

被引：12
作者：
Lavoie, R. Gervais [1 ]
Marchildon, L. [1 ]
Rochon, D. [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：
NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-BASIC TOPICS IN PHYSICS | 2010年 / 125卷 / 10期
基金：
加拿大自然科学与工程研究理事会;
关键词：
MECHANICS;
D O I：
10.1393/ncb/i2010-10927-x
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position and momentum operators, and adapting the algebraic treatment of the standard quantum harmonic oscillator, we find eigenvalues and eigenkets of the bicomplex harmonic oscillator Hamiltonian. We construct an infinite-dimensional bicomplex module from these eigenkets. Turning next to the differential equation approach, we obtain coordinate-basis eigenfunctions of the bicomplex harmonic oscillator Hamiltonian in terms of hyperbolic Hermite polynomials.
引用
收藏
页码：1173 / 1192
页数：20
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