| 三维各向同性谐振子在两不同坐标下的解及其联系 |
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| 引用本文： | 付文羽. 三维各向同性谐振子在两不同坐标下的解及其联系[J]. 延安大学学报(自然科学版), 2011, 30(1): 19-22 |
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| 作者姓名： | 付文羽 |
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| 作者单位： | 宁波工程学院理学院,浙江宁波,315211 |
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| 基金项目： | 甘肃省高校研究生导师科研项目计划，宁波工程学院科研启动项目 |
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| 摘 要： | 根据量子理论及薛定谔方程,从三维各向同性谐振子的本征值与本征函数出发,详细研究了三维各向同性谐振子在直角坐标系和球面坐标系下的本征函数、本征值之间的对应关系。理论分析表明,直角坐标系两不同坐标系下的本征函数之间通过一个幺正变换联系起来,能级简并度与幺正变换矩阵阶数相同。
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| 关 键 词： | 量子力学 三维各向同性谐振子 不同坐标系 本征函数 |
Results and Relationship of Three- Dimensional Isotropic Harmonic Oscillator in the Two Different Coordinate Systems |
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| FU Wen-yu. Results and Relationship of Three- Dimensional Isotropic Harmonic Oscillator in the Two Different Coordinate Systems[J]. Journal of Yan'an University(Natural Science Edition), 2011, 30(1): 19-22 |
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| Authors: | FU Wen-yu |
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| Affiliation: | FU Wen-yu(Faculty of Science,Ning bo University of Technology,Ning bo 315211,China) |
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| Abstract: | Based on the theory of quantum and schrodinger function,it discussed particularly the corresponding relationship of eigenfunctions and eigenvalue for three-dimensional isotropic harmonic oscillator in cartesian coordinate and in spherical coordinate respectively.The theoretical results show that the eigenfunctions in cartesian coordinate and in spherical coordinate are associated by unitary transformation,and the degeneracy of energy level is same with the order of unitary transformation. |
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| Keywords: | quantum mechanics three-dimensional isotropic harmonic oscillator different coordinate systems eigenfunction. |
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