【摘要】 各向同性谐振子是量子理论中能够严格求解的可解势场之一.对它的研究和讨论,在理论上和实际的应用中都有重要意义.本文推导出了N维(N≥2)各向同性谐振子径向矩阵元〈nrl|rk|nr′l′〉的递推公式,在此基础上得到了平均值的递推公式,并且讨论了维各向同性谐振子径向矩阵元的递推公式的一般性,而文献[3]与[4]所给出的各向同性谐振子径向矩阵元的递推公式只是本文结论的特例.更多还原

【Abstract】 The isotropic harmonic oscillator is one of the potential fields with strict solution.There is important significance to discuss and study it in theory and application.In this paper the recurrence formula for radial matrix elements 〈n_rl｜r~k｜n′_rl′〉 of N-dimensional isotropic harmonic oscillator is derived and on the basis of it we obtain the recurrence formula for the expectation values.We discuss the common property of the recurrence formula for radial matrix elements,however,in Refs[3] and [4] the recurrence formula for radial matrix elements are only the examples of the result in this paper.更多还原