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根据广义Laguerre多项式的数学性质,导出了较为简单的三维各向同性谐振子径向矩阵元的普遍公式,并在这基础上计算了一些重要特殊情形的径向矩阵元: 矢径r整数次幂的平均值,电偶极跃迁矩阵元和电四极跃迁矩阵元.
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关键词:
- 三维各向同性谐振子 /
- 径向矩阵元 /
- 广义Laguerre多项式 /
- 偶极跃迁 /
- 四极跃迁
A concise general formula of the radial matrix element of the three-dimensional isotropic oscillator is derived using the properties of the general Laguerre polynomials. Some important special cases, such as the average value of the integer power of radial vector, the matrix element of the electric dipole transition and the element of the electric quadrupole transition, are obtained from the general formula.-
Keywords:
- three-dimensional isotropic oscillator /
- radial matrix element /
- general Laguerre polynomials /
- dipole transition /
- quadrupole transition
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