Research on the Dynamic Problems of 3D Cross Coupling Quantum Harmonic Oscillator by Virtue of Intermediate Representation |x〉λ,ν

被引:0
作者
Shi-Min Xu
Xing-Lei Xu
Hong-Qi Li
机构
[1] Heze University,Department of Physics
[2] Heze University,Key Laboratory of Quantum Communication and Calculation
来源
International Journal of Theoretical Physics | 2008年 / 47卷
关键词
Intermediate representation; Quadratic form;
D O I
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中图分类号
学科分类号
摘要
The intermediate representation (namely intermediate coordinate-momentum representation) |x〉λ,ν are introduced and employed to research the expression of the operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau\hat{p}+\sigma\hat{x}$\end{document} in intermediate representation |x〉λ,ν. The systematic Hamilton operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat{H}$\end{document} of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ,ν,τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator |x〉λ,νλ,ν〈x|, and the Radon transformation of Wigner function is just a margin distribution.
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页码:1654 / 1662
页数:8
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