Hilbert Space of the Bicomplex Quantum Harmonic Oscillator

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
ADVANCES IN QUANTUM THEORY | 2011年 / 1327卷
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; modules; Hilbert spaces; harmonic oscillator; MECHANICS;
D O I
10.1063/1.3567438
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Bicomplex numbers are pairs of complex numbers with a multiplication law that makes them a commutative ring. The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers. Starting with the commutator of the bicomplex position and momentum operators, we find eigenvalues and eigenkets of the bicomplex harmonic oscillator Hamiltonian. Coordinate-basis eigenfunctions of the Hamiltonian are then obtained in terms of hyperbolic Hermite polynomials, and some of them are graphically illustrated. These eigenfunctions form a basis of an infinite-dimensional module over bicomplex numbers, and this module can be given the structure of a bicomplex Hilbert space.
引用
收藏
页码:148 / +
页数:2
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