大学物理 ›› 2012, Vol. 31 ›› Issue (9): 7-7.
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刘丽彦[1] 魏莉倩[2]
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摘要： 通过构造哈密顿量与谐振子系统哈密顿量对易的超对称系统，量子谐振子的性质就可以通过对超对称系统的研究来得到．利用超对称系统的性质，在没有用到厄米多项式的情况下，给出了谐振子本征函数中展开系数问的递推关系，由递推关系可以直接得到本征函数．此方法下得到的归一化本征函数与用厄米多项式表达的本征函数完全相同，并且本征函数的宇称可以明显的显示出来.
关键词: 量子谐振子, 薛定谔方程, 本征函数, 超对称系统
Abstract: By constructing the supersymmetric system which Hamiltonian commutates with that of harmonic os-cillator, the properties of harmonic oscillator can be obtained through the investigation of supersymmetric system. Based on the property of supersymmetric system, the recursion relation between the expanding parameter in the ei-genfunction of harmonic oscillator is obtained without using the theory of Hermite polynomials, then the eigenfunc-tion can be directly found from the recursion relation. The normalized eigenfunction obtained is actually the same as that represented through Hermite polynomials, and the parity of the eigenfunction can be evidently exhibited.
Key words: quantum harmonic oscillator, Schrtidinger equation, eigenfunction, supersymmetric system
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刘丽彦[] 魏莉倩[]. 谐振子薛定谔方程的超对称解法[J]. 大学物理, 2012, 31(9): 7-7.
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